Question

find the unknown side lengths labeled with a variable in the given pair of similar triangles.
image of two triangles: first triangle with sides 15 cm, 15 cm, 18 cm; second triangle with sides 5 cm, a, b

a = 5 cm
b = \square cm

Explanation:

Step1: Find the scale factor

The first triangle has a side of 15 cm, and the corresponding side in the second triangle is 5 cm. The scale factor is $\frac{5}{15}=\frac{1}{3}$.

Step2: Calculate the length of \( b \)

The side of length 18 cm in the first triangle corresponds to side \( b \) in the second triangle. Using the scale factor, we have \( b = 18\times\frac{1}{3}=6 \).

Answer:

\( b = 6 \) cm