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 scale factor

First, find the smallest side of △EFG: 56. The smallest side of △QRS is 140. Calculate the scale factor:
$\text{Scale factor} = \frac{140}{56} = 2.5$

Step2: Find longest side of △QRS

The longest side of △EFG is 72. Multiply by the scale factor:
$\text{Longest side of QRS} = 72 \times 2.5 = 180$

Answer:

B. 180