Question

triangles efg and qrs are similar. the lengths of the sides of efg are 72, 64, and 56. the length of the smallest side of qrs is 140, what is the length of the longest side of qrs? a 120 b 180 c 240 d 360

Explanation:

Step1: Identify sides of EFG

The sides of triangle EFG are 72, 64, and 56. The smallest side is 56, and the longest side is 72.

Step2: Set up proportion for similar triangles

Since triangles EFG and QRS are similar, the ratios of corresponding sides are equal. Let \( x \) be the longest side of QRS. The proportion is \(\frac{\text{Smallest side of EFG}}{\text{Smallest side of QRS}}=\frac{\text{Longest side of EFG}}{\text{Longest side of QRS}}\), so \(\frac{56}{140}=\frac{72}{x}\).

Step3: Solve for \( x \)

Cross - multiply: \( 56x = 140\times72 \). Then \( x=\frac{140\times72}{56} \). Simplify \( 140\div56 = 2.5 \), so \( x = 2.5\times72=180 \).

Answer:

B. 180