Question

figure stuv and figure wxyz, shown below, are similar figures. the scale factor of figure stuv to figure wxyz is 3:1. if st = 78 mm and sv = 102 mm, what is the length of side wx? a. 34 mm b. 306 mm c. 26 mm d. 234 mm

Explanation:

Step1: Recall scale - factor formula

For similar figures, if the scale factor of figure 1 to figure 2 is \(k\), and a side length of figure 1 is \(a\) and the corresponding side length of figure 2 is \(b\), then \(k=\frac{a}{b}\). Here, \(k = 3\), \(a = ST\), and \(b = WX\).

Step2: Rearrange the formula to solve for \(WX\)

We have \(3=\frac{ST}{WX}\), so \(WX=\frac{ST}{3}\).

Step3: Substitute the value of \(ST\)

Given \(ST = 78\) mm, then \(WX=\frac{78}{3}=26\) mm.

Answer:

C. 26 mm