Question

1. the pentagons below are similar. what is the value of x? (with two pentagons: one has a side 5 mm and a base x mm, the other has a corresponding side 20 mm and a corresponding base 24 mm) answer

Explanation:

Step1: Set up proportion for similar figures

Since the pentagons are similar, the ratios of corresponding sides are equal. So, $\frac{5}{20}=\frac{x}{24}$.

Step2: Solve for x

Cross - multiply: $20x = 5\times24$.
Calculate $5\times24 = 120$. Then, $20x=120$.
Divide both sides by 20: $x=\frac{120}{20}=6$.

Answer:

6