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, 6.9], [0.0, 0.0], [5.94, 3.512], [5.94, 10.412], [0.0, 6.9]]], [[[2.97, 5.206], [2.475, 5.488333333333333], [2.192619904641739, 4.9933600079343075], [2.687619904641739, 4.711026674600974], [2.97, 5.206]]]], "init": {"range": [[-1.0, 6.94], [-1.0, 11.412]], "scale": [45, 45]}, "arc": [[[0.0, 0.0], [1.1500000000000001, 1.1500000000000001], 30.593523523463602, 90.0, false], [[5.94, 10.412], [1.1500000000000001, 1.1500000000000001], 210.59352352346355, 270.0, false], [[5.94, 3.512], [1.1500000000000001, 1.1500000000000001], 90.0, 210.59352352346355, false], [[5.94, 3.512], [0.9200000000000002, 0.9200000000000002], 90.0, 210.59352352346355, false], [[0.0, 6.9], [1.1500000000000001, 1.1500000000000001], 270.0, 30.593523523463602, false], [[0.0, 6.9], [0.9200000000000002, 0.9200000000000002], 270.0, 30.593523523463602, false]], "line": [[[0.23, 3.22], [-0.23, 3.68]], [[0.23, 3.45], [-0.23, 3.91]], [[0.23, 2.99], [-0.23, 3.45]], [[0.0, 6.9], [0.0, 0.0], {"subtype": "segment"}], [[3.0509267520343837, 2.071041046222814], [2.8890732479656167, 1.4409589537771859]], [[2.8529428529057848, 1.9539838991285987], [2.691089348837018, 1.3239018066829704]], [[3.2489106511629826, 2.1880981933170296], [3.0870571470942156, 1.5580161008714013]], [[0.0, 0.0], [5.94, 3.512], {"subtype": "segment"}], [[6.170000000000001, 6.732], [5.71, 7.192000000000001]], [[6.170000000000001, 6.962000000000001], [5.71, 7.4220000000000015]], [[6.170000000000001, 6.502], [5.71, 6.962000000000001]], [[5.94, 3.512], [5.94, 10.412], {"subtype": "segment"}], [[2.8890732479656167, 8.340958953777186], [3.0509267520343837, 8.971041046222815]], [[3.0870571470942156, 8.4580161008714], [3.2489106511629826, 9.08809819331703]], [[2.691089348837018, 8.22390180668297], [2.8529428529057848, 8.8539838991286]], [[5.94, 10.412], [0.0, 6.9], {"subtype": "segment"}], [[0.0, 6.9], [5.94, 3.512], {"opacity": 0.3, "subtype": "segment", "stroke-dasharray": "- "}], [[0.0, 0.0], [5.94, 10.412], {"opacity": 0.3, "subtype": "segment", "stroke-dasharray": "- "}]], "label": [[[0.569833925020379, 0.9988940373712667], "59\u00b0", "above right"], [[5.370166074979621, 9.413105962628734], "59\u00b0", "below left"], [[4.9411059626287335, 4.081833925020378], "121\u00b0", "above left"], [[0.9988940373712665, 6.330166074979621], "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, 4.140000000000001], [0.0, 0.0], [3.564000000000001, 2.1072], [3.564000000000001, 6.247200000000001], [0.0, 4.140000000000001]]], [[[1.7820000000000005, 3.1236000000000006], [1.4850000000000003, 3.2930000000000006], [1.3155719427850436, 2.996016004760585], [1.6125719427850438, 2.826616004760585], [1.7820000000000005, 3.1236000000000006]]]], "init": {"range": [[-1.0, 4.564000000000001], [-1.0, 7.247200000000001]], "scale": [45, 45]}, "arc": [[[0.0, 0.0], [0.6900000000000001, 0.6900000000000001], 30.593523523463602, 90.0, false], [[3.564000000000001, 6.247200000000001], [0.6900000000000001, 0.6900000000000001], 210.59352352346355, 270.0, false], [[3.564000000000001, 2.1072], [0.6900000000000001, 0.6900000000000001], 90.0, 210.59352352346355, false], [[3.564000000000001, 2.1072], [0.552, 0.552], 90.0, 210.59352352346355, false], [[0.0, 4.140000000000001], [0.6900000000000001, 0.6900000000000001], 270.0, 30.593523523463602, false], [[0.0, 4.140000000000001], [0.552, 0.552], 270.0, 30.593523523463602, false]], "line": [[[0.13666666666666666, 1.9333333333333336], [-0.13666666666666666, 2.206666666666667]], [[0.0, 4.140000000000001], [0.0, 0.0], {"subtype": "segment"}], [[1.8300869106291269, 1.2407983028280491], [1.733913089370874, 0.866401697171951]], [[0.0, 0.0], [3.564000000000001, 2.1072], {"subtype": "segment"}], [[3.7006666666666677, 4.040533333333334], [3.4273333333333342, 4.313866666666668]], [[3.564000000000001, 2.1072], [3.564000000000001, 6.247200000000001], {"subtype": "segment"}], [[1.733913089370874, 5.006401697171952], [1.8300869106291269, 5.38079830282805]], [[3.564000000000001, 6.247200000000001], [0.0, 4.140000000000001], {"subtype": "segment"}], [[0.0, 4.140000000000001], [3.564000000000001, 2.1072], {"opacity": 0.3, "subtype": "segment", "stroke-dasharray": "- "}], [[0.0, 0.0], [3.564000000000001, 6.247200000000001], {"opacity": 0.3, "subtype": "segment", "stroke-dasharray": "- "}]], "label": [[[0.3419003550122274, 0.59933642242276], "59\u00b0", "above right"], [[3.2220996449877735, 5.647863577577241], "59\u00b0", "below left"], [[2.964663577577241, 2.4491003550122272], "121\u00b0", "above left"], [[0.5993364224227596, 3.7980996449877726], "121\u00b0", "below right"]]}
B.

{"path": [[[[0.0, 7.590000000000001], [0.0, 0.0], [6.534000000000001, 3.8632000000000004], [6.534000000000001, 11.453200000000002], [0.0, 7.590000000000001]]], [[[3.2670000000000003, 5.726600000000001], [2.7225, 6.037166666666668], [2.411881895105913, 5.492696008727739], [2.956381895105913, 5.182129342061073], [3.2670000000000003, 5.726600000000001]]]], "init": {"range": [[-1.0, 7.534000000000001], [-1.0, 12.453200000000002]], "scale": [45, 45]}, "arc": [[[0.0, 0.0], [1.2650000000000001, 1.2650000000000001], 30.593523523463602, 90.0, false], [[6.534000000000001, 11.453200000000002], [1.2650000000000003, 1.2650000000000003], 210.59352352346355, 270.0, false], [[6.534000000000001, 3.8632000000000004], [1.2650000000000003, 1.2650000000000003], 90.0, 210.59352352346355, false], [[6.534000000000001, 3.8632000000000004], [1.0120000000000002, 1.0120000000000002], 90.0, 210.59352352346355, false], [[0.0, 7.590000000000001], [1.2650000000000001, 1.2650000000000001], 270.0, 30.593523523463602, false], [[0.0, 7.590000000000001], [1.0120000000000002, 1.0120000000000002], 270.0, 30.593523523463602, false]], "line": [[[0.2533333333333333, 3.541666666666667], [-0.2533333333333333, 4.048333333333334]], [[0.0, 7.590000000000001], [0.0, 0.0], {"subtype": "segment"}], [[3.356136712385698, 2.2786017320715057], [3.1778632876143025, 1.5845982679284947]], [[0.0, 0.0], [6.534000000000001, 3.8632000000000004], {"subtype": "segment"}], [[6.787333333333334, 7.404866666666669], [6.280666666666668, 7.911533333333335]], [[6.534000000000001, 3.8632000000000004], [6.534000000000001, 11.453200000000002], {"subtype": "segment"}], [[3.1778632876143025, 9.174598267928495], [3.356136712385698, 9.868601732071507]], [[6.534000000000001, 11.453200000000002], [0.0, 7.590000000000001], {"subtype": "segment"}], [[0.0, 7.590000000000001], [6.534000000000001, 3.8632000000000004], {"opacity": 0.3, "subtype": "segment", "stroke-dasharray": "- "}], [[0.0, 0.0], [6.534000000000001, 11.453200000000002], {"opacity": 0.3, "subtype": "segment", "stroke-dasharray": "- "}]], "label": [[[0.6268173175224168, 1.0987834411083932], "59\u00b0", "above right"], [[5.907182682477583, 10.354416558891609], "59\u00b0", "below left"], [[5.435216558891607, 4.490017317522417], "121\u00b0", "above left"], [[1.0987834411083937, 6.963182682477584], "121\u00b0", "below right"]]}
C.

{"path": [[[[0.0, 5.47], [0.0, 0.0], [5.468, 0.155], [5.468, 5.625], [0.0, 5.47]]], [[[2.734, 2.8125], [2.2783333333333333, 3.2554166666666666], [1.8354002973607721, 2.7997659118485143], [2.2910669640274386, 2.3568492451818477], [2.734, 2.8125]]]], "init": {"range": [[-1.0, 6.468], [-1.0, 6.625]], "scale": [45, 45]}, "arc": [[[0.0, 0.0], [0.9116666666666666, 0.9116666666666666], 1.6237140219196817, 90.0, false], [[5.468, 5.625], [0.9116666666666666, 0.9116666666666666], 181.62371402191968, 270.0, false], [[5.468, 0.155], [0.9116666666666666, 0.9116666666666666], 90.0, 181.62371402191968, false], [[5.468, 0.155], [0.7293333333333334, 0.7293333333333334], 90.0, 181.62371402191968, false], [[0.0, 5.47], [0.9116666666666666, 0.9116666666666666], 270.0, 1.6237140219196817, false], [[0.0, 5.47], [0.7293333333333334, 0.7293333333333334], 270.0, 1.6237140219196817, false]], "line": [[[0.18333333333333332, 2.5516666666666667], [-0.18333333333333332, 2.918333333333333]], [[0.18333333333333332, 2.735], [-0.18333333333333332, 3.101666666666666]], [[0.0, 5.47], [0.0, 0.0], {"subtype": "segment"}], [[2.912064903552249, 0.26595453654701584], [2.555935096447751, -0.11095453654701586]], [[2.7288051835026166, 0.2607597200496323], [2.3726753763981185, -0.11614935304439936]], [[0.0, 0.0], [5.468, 0.155], {"subtype": "segment"}], [[5.6513333333333335, 2.706666666666667], [5.284666666666666, 3.0733333333333333]], [[5.6513333333333335, 2.89], [5.284666666666666, 3.2566666666666664]], [[5.468, 0.155], [5.468, 5.625], {"subtype": "segment"}], [[2.555935096447751, 5.359045463452984], [2.912064903552249, 5.735954536547015]], [[2.7391948164973834, 5.3642402799503675], [3.0953246236018814, 5.741149353044399]], [[5.468, 5.625], [0.0, 5.47], {"subtype": "segment"}], [[0.0, 5.47], [5.468, 0.155], {"opacity": 0.3, "subtype": "segment", "stroke-dasharray": "- "}], [[0.0, 0.0], [5.468, 5.625], {"opacity": 0.3, "subtype": "segment", "stroke-dasharray": "- "}]], "label": [[[0.6354469167203916, 0.6537150198225973], "88\u00b0", "above right"], [[4.832553083279609, 4.971284980177402], "88\u00b0", "below left"], [[4.814284980177403, 0.7904469167203916], "92\u00b0", "above left"], [[0.6537150198225975, 4.834553083279609], "92\u00b0", "below right"]]}
D.

{"path": [[[[0.0, 7.3500000000000005], [0.0, 0.0], [5.303, 5.089], [5.303, 12.439], [0.0, 7.3500000000000005]]], [[[2.6515, 6.2195], [2.2095833333333332, 6.407916666666667], [2.021182369733454, 5.965993305131895], [2.463099036400121, 5.777576638465228], [2.6515, 6.2195]]]], "init": {"range": [[-1.0, 6.303], [-1.0, 13.439]], "scale": [45, 45]}, "arc": [[[0.0, 0.0], [1.2249685937017143, 1.2249685937017143], 43.8202882916043, 90.0, false], [[5.303, 12.439], [1.2249685937017143, 1.2249685937017143], 223.82028829160436, 270.0, false], [[5.303, 5.089], [1.2249685937017143, 1.2249685937017143], 90.0, 223.82028829160436, false], [[5.303, 5.089], [0.9799748749613715, 0.9799748749613715], 90.0, 223.82028829160436, false], [[0.0, 7.3500000000000005], [1.2249685937017143, 1.2249685937017143], 270.0, 43.8202882916043, false], [[0.0, 7.3500000000000005], [0.9799748749613715, 0.9799748749613715], 270.0, 43.8202882916043, false]], "line": [[[0.24333333333333332, 3.431666666666667], [-0.24333333333333332, 3.9183333333333334]], [[0.0, 7.3500000000000005], [0.0, 0.0], {"subtype": "segment"}], [[2.6585849888997255, 2.8885523581586283], [2.6444150111002744, 2.200447641841372]], [[2.483016315370549, 2.720068673529177], [2.468846337571098, 2.0319639572119206]], [[0.0, 0.0], [5.303, 5.089], {"subtype": "segment"}], [[5.546333333333333, 8.520666666666665], [5.059666666666667, 9.007333333333333]], [[5.303, 5.089], [5.303, 12.439], {"subtype": "segment"}], [[2.6444150111002744, 9.550447641841373], [2.6585849888997255, 10.238552358158628]], [[2.8199836846294515, 9.718931326470825], [2.8341536624289025, 10.40703604278808]], [[5.303, 12.439], [0.0, 7.3500000000000005], {"subtype": "segment"}], [[0.0, 7.3500000000000005], [5.303, 5.089], {"opacity": 0.3, "subtype": "segment", "stroke-dasharray": "- "}], [[0.0, 0.0], [5.303, 12.439], {"opacity": 0.3, "subtype": "segment", "stroke-dasharray": "- "}]], "label": [[[0.4804011483459517, 1.126837518111394], "46\u00b0", "above right"], [[4.822598851654048, 11.312162481888606], "46\u00b0", "below left"], [[4.176162481888605, 5.569401148345951], "134\u00b0", "above left"], [[1.1268375181113937, 6.8695988516540485], "134\u00b0", "below right"]]}

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