Proportionnalité

Pour aller plus loin (Ancien programme) - Mathématiques 5e

Exemple d'exercice parmi les 105 exercices du chapitre

On considère la figure modèle suivante :

{"path": [[[[0.0, 5.4], [0.0, 0.0], [4.64, 2.763], [4.64, 8.163], [0.0, 5.4]]], [[[2.32, 4.0815], [1.9333333333333331, 4.3012500000000005], [1.7135542521648301, 3.914599862159808], [2.1002209188314964, 3.694849862159808], [2.32, 4.0815]]]], "init": {"range": [[-1.0, 5.64], [-1.0, 9.163]], "scale": [45, 45]}, "arc": [[[0.0, 0.0], [0.9, 0.9], 30.772704591657487, 90.0, false], [[4.64, 8.163], [0.9, 0.9], 210.77270459165754, 270.0, false], [[4.64, 2.763], [0.9, 0.9], 90.0, 210.77270459165754, false], [[4.64, 2.763], [0.7200000000000001, 0.7200000000000001], 90.0, 210.77270459165754, false], [[0.0, 5.4], [0.9, 0.9], 270.0, 30.772704591657487, false], [[0.0, 5.4], [0.7200000000000001, 0.7200000000000001], 270.0, 30.772704591657487, false]], "line": [[[0.18000000000000002, 2.52], [-0.18000000000000002, 2.8800000000000003]], [[0.18000000000000002, 2.7], [-0.18000000000000002, 3.0600000000000005]], [[0.18000000000000002, 2.34], [-0.18000000000000002, 2.7]], [[0.0, 5.4], [0.0, 0.0], {"subtype": "segment"}], [[2.3825626236126625, 1.6282507206204275], [2.257437376387337, 1.1347492793795724]], [[2.2279059514961173, 1.5361566721165452], [2.102780704270792, 1.04265523087569]], [[2.5372192957292077, 1.72034476912431], [2.4120940485038824, 1.2268433278834547]], [[0.0, 0.0], [4.64, 2.763], {"subtype": "segment"}], [[4.819999999999999, 5.283], [4.46, 5.643]], [[4.819999999999999, 5.463], [4.46, 5.8229999999999995]], [[4.819999999999999, 5.103000000000001], [4.46, 5.463]], [[4.64, 2.763], [4.64, 8.163], {"subtype": "segment"}], [[2.257437376387337, 6.5347492793795725], [2.3825626236126625, 7.028250720620428]], [[2.4120940485038824, 6.626843327883455], [2.5372192957292077, 7.12034476912431]], [[2.102780704270792, 6.44265523087569], [2.2279059514961173, 6.936156672116546]], [[4.64, 8.163], [0.0, 5.4], {"subtype": "segment"}], [[0.0, 5.4], [4.64, 2.763], {"opacity": 0.3, "subtype": "segment", "stroke-dasharray": "- "}], [[0.0, 0.0], [4.64, 8.163], {"opacity": 0.3, "subtype": "segment", "stroke-dasharray": "- "}]], "label": [[[0.44473406758001416, 0.7824395242660837], "59\u00b0", "above right"], [[4.195265932419986, 7.380560475733916], "59\u00b0", "below left"], [[3.8575604757339157, 3.207734067580014], "121\u00b0", "above left"], [[0.7824395242660834, 4.9552659324199855], "121\u00b0", "below right"]]}

Parmi les figures A, B, C, D ci-dessous, lesquelles sont des agrandissements ou des réductions de la figure modèle.

A.

{"path": [[[[0.0, 4.32], [0.0, 0.0], [3.7119999999999997, 2.2104], [3.7119999999999997, 6.5304], [0.0, 4.32]]], [[[1.8559999999999999, 3.2652], [1.5466666666666664, 3.4410000000000003], [1.370843401731864, 3.131679889727846], [1.6801767350651973, 2.9558798897278464], [1.8559999999999999, 3.2652]]]], "init": {"range": [[-1.0, 4.712], [-1.0, 7.5304]], "scale": [45, 45]}, "arc": [[[0.0, 0.0], [0.7200000000000001, 0.7200000000000001], 30.772704591657487, 90.0, false], [[3.7119999999999997, 6.5304], [0.7200000000000001, 0.7200000000000001], 210.77270459165754, 270.0, false], [[3.7119999999999997, 2.2104], [0.7200000000000001, 0.7200000000000001], 90.0, 210.77270459165754, false], [[3.7119999999999997, 2.2104], [0.5760000000000001, 0.5760000000000001], 90.0, 210.77270459165754, false], [[0.0, 4.32], [0.7200000000000001, 0.7200000000000001], 270.0, 30.772704591657487, false], [[0.0, 4.32], [0.5760000000000001, 0.5760000000000001], 270.0, 30.772704591657487, false]], "line": [[[0.1433333333333333, 2.0166666666666666], [-0.1433333333333333, 2.3033333333333337]], [[0.1433333333333333, 2.16], [-0.1433333333333333, 2.446666666666667]], [[0.1433333333333333, 1.8733333333333333], [-0.1433333333333333, 2.16]], [[0.0, 4.32], [0.0, 0.0], {"subtype": "segment"}], [[1.9058183854693425, 1.3016866849384885], [1.8061816145306573, 0.9087133150615114]], [[1.782665850265427, 1.2283525352039155], [1.6830290793267417, 0.8353791653269385]], [[2.028970920673258, 1.3750208346730615], [1.9293341497345728, 0.9820474647960844]], [[0.0, 0.0], [3.7119999999999997, 2.2104], {"subtype": "segment"}], [[3.8553333333333333, 4.2270666666666665], [3.568666666666666, 4.513733333333334]], [[3.8553333333333333, 4.3704], [3.568666666666666, 4.657066666666667]], [[3.8553333333333333, 4.083733333333333], [3.568666666666666, 4.3704]], [[3.7119999999999997, 2.2104], [3.7119999999999997, 6.5304], {"subtype": "segment"}], [[1.8061816145306573, 5.228713315061512], [1.9058183854693425, 5.6216866849384886]], [[1.9293341497345728, 5.302047464796085], [2.028970920673258, 5.695020834673062]], [[1.6830290793267417, 5.155379165326939], [1.782665850265427, 5.548352535203915]], [[3.7119999999999997, 6.5304], [0.0, 4.32], {"subtype": "segment"}], [[0.0, 4.32], [3.7119999999999997, 2.2104], {"opacity": 0.3, "subtype": "segment", "stroke-dasharray": "- "}], [[0.0, 0.0], [3.7119999999999997, 6.5304], {"opacity": 0.3, "subtype": "segment", "stroke-dasharray": "- "}]], "label": [[[0.3557872540640114, 0.625951619412867], "59\u00b0", "above right"], [[3.3562127459359883, 5.904448380587134], "59\u00b0", "below left"], [[3.0860483805871324, 2.566187254064011], "121\u00b0", "above left"], [[0.625951619412867, 3.9642127459359893], "121\u00b0", "below right"]]}
B.

{"path": [[[[0.0, 7.45], [0.0, 0.0], [6.471, 3.692], [6.471, 11.142], [0.0, 7.45]]], [[[3.2355, 5.571], [2.69625, 5.884166666666666], [2.383071001200465, 5.344923828678037], [2.922321001200465, 5.03175716201137], [3.2355, 5.571]]]], "init": {"range": [[-1.0, 7.471], [-1.0, 12.142]], "scale": [45, 45]}, "arc": [[[0.0, 0.0], [1.2416666666666667, 1.2416666666666667], 29.70672545174574, 90.0, false], [[6.471, 11.142], [1.2416666666666665, 1.2416666666666665], 209.7067254517458, 270.0, false], [[6.471, 3.692], [1.2416666666666665, 1.2416666666666665], 90.0, 209.7067254517458, false], [[6.471, 3.692], [0.9933333333333332, 0.9933333333333332], 90.0, 209.7067254517458, false], [[0.0, 7.45], [1.2416666666666667, 1.2416666666666667], 270.0, 29.70672545174574, false], [[0.0, 7.45], [0.9933333333333334, 0.9933333333333334], 270.0, 29.70672545174574, false]], "line": [[[0.25, 3.475], [-0.25, 3.975]], [[0.0, 7.45], [0.0, 0.0], {"subtype": "segment"}], [[3.328753181197042, 2.1870334942445266], [3.142246818802958, 1.5049665057554735]], [[0.0, 0.0], [6.471, 3.692], {"subtype": "segment"}], [[6.721, 7.167], [6.221, 7.667]], [[6.471, 3.692], [6.471, 11.142], {"subtype": "segment"}], [[3.142246818802958, 8.954966505755472], [3.328753181197042, 9.637033494244527]], [[6.471, 11.142], [0.0, 7.45], {"subtype": "segment"}], [[0.0, 7.45], [6.471, 3.692], {"opacity": 0.3, "subtype": "segment", "stroke-dasharray": "- "}], [[0.0, 0.0], [6.471, 11.142], {"opacity": 0.3, "subtype": "segment", "stroke-dasharray": "- "}]], "label": [[[0.6235833539374132, 1.0737224556668628], "60\u00b0", "above right"], [[5.8474166460625865, 10.068277544333137], "60\u00b0", "below left"], [[5.3972775443331376, 4.315583353937413], "120\u00b0", "above left"], [[1.073722455666863, 6.8264166460625875], "120\u00b0", "below right"]]}
C.

{"path": [[[[0.0, 4.75], [0.0, 0.0], [4.126, 2.353], [4.126, 7.103], [0.0, 4.75]]], [[[2.063, 3.5515], [1.7191666666666667, 3.7512499999999998], [1.5194343423691774, 3.407406398573663], [1.8632676757025108, 3.207656398573663], [2.063, 3.5515]]]], "init": {"range": [[-1.0, 5.126], [-1.0, 8.103]], "scale": [45, 45]}, "arc": [[[0.0, 0.0], [0.791631315000164, 0.791631315000164], 29.69550645347084, 90.0, false], [[4.126, 7.103], [0.791631315000164, 0.791631315000164], 209.69550645347078, 270.0, false], [[4.126, 2.353], [0.791631315000164, 0.791631315000164], 90.0, 209.6955064534709, false], [[4.126, 2.353], [0.6333050520001313, 0.6333050520001313], 90.0, 209.6955064534709, false], [[0.0, 4.75], [0.791631315000164, 0.791631315000164], 270.0, 29.69550645347084, false], [[0.0, 4.75], [0.6333050520001313, 0.6333050520001313], 270.0, 29.69550645347084, false]], "line": [[[0.15666666666666668, 2.2183333333333333], [-0.15666666666666668, 2.5316666666666667]], [[0.15666666666666668, 2.375], [-0.15666666666666668, 2.6883333333333335]], [[0.0, 4.75], [0.0, 0.0], {"subtype": "segment"}], [[2.1214805061684436, 1.3902028761789873], [2.0045194938315567, 0.9627971238210129]], [[1.985388814994728, 1.3125916911737154], [1.8684278026578416, 0.885185938815741]], [[2.2575721973421587, 1.4678140611842592], [2.140611185005272, 1.0404083088262848]], [[0.0, 0.0], [4.126, 2.353], {"subtype": "segment"}], [[4.282666666666667, 4.5713333333333335], [3.9693333333333336, 4.884666666666666]], [[4.282666666666667, 4.728], [3.9693333333333336, 5.041333333333332]], [[4.126, 2.353], [4.126, 7.103], {"subtype": "segment"}], [[2.0045194938315567, 5.712797123821012], [2.1214805061684436, 6.1402028761789875]], [[2.140611185005272, 5.790408308826284], [2.2575721973421587, 6.217814061184259]], [[1.8684278026578416, 5.635185938815741], [1.985388814994728, 6.062591691173716]], [[4.126, 7.103], [0.0, 4.75], {"subtype": "segment"}], [[0.0, 4.75], [4.126, 2.353], {"opacity": 0.3, "subtype": "segment", "stroke-dasharray": "- "}], [[0.0, 0.0], [4.126, 7.103], {"opacity": 0.3, "subtype": "segment", "stroke-dasharray": "- "}]], "label": [[[0.39763596722148054, 0.684518645809394], "60\u00b0", "above right"], [[3.72836403277852, 6.418481354190606], "60\u00b0", "below left"], [[3.441481354190606, 2.7506359672214806], "120\u00b0", "above left"], [[0.6845186458093941, 4.35236403277852], "120\u00b0", "below right"]]}
D.

{"path": [[[[0.0, 7.0200000000000005], [0.0, 0.0], [6.032, 3.5919], [6.032, 10.6119], [0.0, 7.0200000000000005]]], [[[3.016, 5.30595], [2.5133333333333336, 5.5916250000000005], [2.2276205278142793, 5.088979820807751], [2.7302871944809457, 4.8033048208077505], [3.016, 5.30595]]]], "init": {"range": [[-1.0, 7.032], [-1.0, 11.6119]], "scale": [45, 45]}, "arc": [[[0.0, 0.0], [1.1700000000000002, 1.1700000000000002], 30.772704591657487, 90.0, false], [[6.032, 10.6119], [1.1700000000000002, 1.1700000000000002], 210.77270459165754, 270.0, false], [[6.032, 3.5919], [1.1700000000000002, 1.1700000000000002], 90.0, 210.77270459165754, false], [[6.032, 3.5919], [0.9360000000000002, 0.9360000000000002], 90.0, 210.77270459165754, false], [[0.0, 7.0200000000000005], [1.1700000000000002, 1.1700000000000002], 270.0, 30.772704591657487, false], [[0.0, 7.0200000000000005], [0.9360000000000002, 0.9360000000000002], 270.0, 30.772704591657487, false]], "line": [[[0.23333333333333334, 3.276666666666667], [-0.23333333333333334, 3.7433333333333336]], [[0.23333333333333334, 3.5100000000000002], [-0.23333333333333334, 3.976666666666667]], [[0.23333333333333334, 3.0433333333333334], [-0.23333333333333334, 3.5100000000000002]], [[0.0, 7.0200000000000005], [0.0, 0.0], {"subtype": "segment"}], [[3.097099697275674, 2.1158120452487026], [2.934900302724326, 1.4760879547512975]], [[2.8966188260134857, 1.996430871262188], [2.7344194314621375, 1.3567067807647832]], [[3.2975805685378625, 2.2351932192352164], [3.1353811739865143, 1.5954691287378118]], [[0.0, 0.0], [6.032, 3.5919], {"subtype": "segment"}], [[6.265333333333333, 6.868566666666667], [5.798666666666667, 7.335233333333334]], [[6.265333333333333, 7.1019000000000005], [5.798666666666667, 7.568566666666667]], [[6.265333333333333, 6.635233333333334], [5.798666666666667, 7.1019000000000005]], [[6.032, 3.5919], [6.032, 10.6119], {"subtype": "segment"}], [[2.934900302724326, 8.496087954751298], [3.097099697275674, 9.135812045248704]], [[3.1353811739865143, 8.615469128737812], [3.2975805685378625, 9.255193219235219]], [[2.7344194314621375, 8.376706780764783], [2.8966188260134857, 9.01643087126219]], [[6.032, 10.6119], [0.0, 7.0200000000000005], {"subtype": "segment"}], [[0.0, 7.0200000000000005], [6.032, 3.5919], {"opacity": 0.3, "subtype": "segment", "stroke-dasharray": "- "}], [[0.0, 0.0], [6.032, 10.6119], {"opacity": 0.3, "subtype": "segment", "stroke-dasharray": "- "}]], "label": [[[0.5781542878540186, 1.017171381545909], "59\u00b0", "above right"], [[5.453845712145981, 9.594728618454091], "59\u00b0", "below left"], [[5.014828618454091, 4.170054287854018], "121\u00b0", "above left"], [[1.0171713815459087, 6.441845712145982], "121\u00b0", "below right"]]}

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