Question

these two polygons are similar. w = ?

Explanation:

Step1: Find the scale - factor

Since the two polygons are similar, the ratios of corresponding sides are equal. We can find the scale - factor by comparing two known corresponding sides. Let's use the sides of length 3 and 15. The scale - factor $k=\frac{15}{3}=5$.

Step2: Calculate the value of $w$

We know that the side of length 2 in the red polygon corresponds to side $w$ in the yellow polygon. Using the scale - factor, we can set up the proportion $\frac{w}{2}=5$. Solving for $w$, we get $w = 2\times5=10$.

Answer:

$10$