Question

b. name possible measures for the sides of $\triangle abc$ using your answer to part a. list the measures in descending order.
18, 12, 12
c. if $\triangle wxy$ is also isosceles and has a perimeter of 28 and $\triangle abc$ has sides with the measures you gave in part b, what must be the measure of the sides of $\triangle wxy$ so that $\triangle wxy sim \triangle abc$? list the measures in descending order.

Explanation:

Step1: Find scale factor $k$

First, calculate the perimeter of $\triangle ABC$: $18 + 12 + 12 = 42$.
Let the scale factor of $\triangle WXY$ to $\triangle ABC$ be $k$. The perimeter of $\triangle WXY$ is 28, so:
$$k = \frac{\text{Perimeter of } \triangle WXY}{\text{Perimeter of } \triangle ABC} = \frac{28}{42} = \frac{2}{3}$$

Step2: Scale each side of $\triangle ABC$

Multiply each side length of $\triangle ABC$ by $k=\frac{2}{3}$:
Longest side: $18 \times \frac{2}{3} = 12$
Equal sides: $12 \times \frac{2}{3} = 8$

Answer:

12, 8, 8