Question

the figures are similar. find the missing side and enter in the pink box.
35, 70,?, 40
the figures are similar. find the missing side and enter in the pink box.
?, 63, 80, 90
the figures are similar. find the missing side and enter in the pink box.
8,?, 3.8, 15.2, 12, 40, 32

Explanation:

Step1: Set up proportion for first problem

For similar rectangles, \(\frac{35}{70}=\frac{x}{40}\)

Step2: Solve for \(x\)

Cross - multiply: \(70x = 35\times40\), \(x=\frac{35\times40}{70}=20\)

Step3: Set up proportion for second problem

For similar triangles, \(\frac{x}{63}=\frac{80}{90}\)

Step4: Solve for \(x\)

Cross - multiply: \(90x = 80\times63\), \(x=\frac{80\times63}{90}=56\)

Step5: Set up proportion for third problem

For similar triangles, \(\frac{8}{15.2}=\frac{y}{32}\)

Step6: Solve for \(y\)

Cross - multiply: \(15.2y=8\times32\), \(y = \frac{8\times32}{15.2}=\frac{256}{15.2}\approx16.84\) (but if using \(\frac{3.8}{40}=\frac{8}{z}\), cross - multiply \(3.8z = 8\times40\), \(z=\frac{8\times40}{3.8}\approx84.21\) (assuming the second triangle's side \(40\) corresponds to the first triangle's side \(3.8\))

Answer:

First problem: \(20\), Second problem: \(56\), Third problem (if side \(40\) corresponds to \(3.8\)): \(\frac{8\times40}{3.8}\approx84.21\) (if side \(32\) corresponds to \(8\)): \(\frac{8\times32}{15.2}\approx16.84\)