Question

these two triangles are similar. find side lengths a and b. note: the two figures are not drawn to scale.

Explanation:

Step1: Set up proportion for side - length a

Since the triangles are similar, the ratios of corresponding sides are equal. For side - length a, we have the proportion $\frac{9}{3}=\frac{a}{5}$.

Step2: Solve for a

Cross - multiply: $9\times5 = 3\times a$, so $45=3a$. Then $a=\frac{45}{3}=15$.

Step3: Set up proportion for side - length b

For side - length b, the proportion is $\frac{b}{5}=\frac{21}{3}$.

Step4: Solve for b

Cross - multiply: $b\times3=21\times5$, so $3b = 105$. Then $b=\frac{105}{3}=35$.

Answer:

$a = 15$, $b = 35$