Question

un pâtissier utilise des moules rectangulaires dont les dimensions sont toutes proportionnelles. le plus petit mesure 16 cm de largeur sur 20 cm de longueur. calcule les dimensions des cinq autres moules sachant que trois ont des largeurs respectives de 12 cm, 18 cm et 28 cm, alors que les deux autres ont des longueurs respectives de 24 cm et 30 cm. réponse:

Explanation:

Step1: Set up proportion

Since the molds are proportion - al, we can set up the proportion using the ratio of length to width. Let the unknown lengths be \(x\) and \(y\). The ratio of length to width for the first - known mold is \(\frac{20}{16}\). For the second mold with width \(12\) cm, we have the proportion \(\frac{20}{16}=\frac{x}{12}\), and for the third mold with width \(18\) cm, we have \(\frac{20}{16}=\frac{y}{18}\).

Step2: Solve for \(x\)

Cross - multiply the first proportion \(\frac{20}{16}=\frac{x}{12}\): \(16x = 20\times12\), so \(16x=240\), and \(x=\frac{240}{16}=15\) cm.

Step3: Solve for \(y\)

Cross - multiply the second proportion \(\frac{20}{16}=\frac{y}{18}\): \(16y = 20\times18\), so \(16y = 360\), and \(y=\frac{360}{16}=22.5\) cm.

Step4: Solve for the other two lengths

For the mold with width \(24\) cm, let the length be \(z\). Using the proportion \(\frac{20}{16}=\frac{z}{24}\), cross - multiply: \(16z=20\times24\), so \(16z = 480\), and \(z = 30\) cm. For the mold with width \(28\) cm, let the length be \(w\). Using the proportion \(\frac{20}{16}=\frac{w}{28}\), cross - multiply: \(16w=20\times28\), so \(16w = 560\), and \(w=\frac{560}{16}=35\) cm.

Answer:

The lengths are \(15\) cm, \(22.5\) cm, \(30\) cm, \(35\) cm.