Question

find the unknown side lengths labeled with a variable in the given pair of similar triangles. a = (simplify your answer. type a whole number.) b = (simplify your answer. type a whole number.)

Explanation:

Step1: Find the scale - factor

Since the two right - angled triangles are similar, the ratios of corresponding sides are equal. The ratio of the vertical sides is $\frac{15}{12}=\frac{5}{4}$.

Step2: Find side length a

We know that $\frac{a}{20}=\frac{15}{12}$. Cross - multiply to get $12a = 15\times20$. Then $a=\frac{15\times20}{12}=\frac{300}{12}=25$.

Step3: Find side length b

We know that $\frac{b}{16}=\frac{15}{12}$. Cross - multiply to get $12b = 15\times16$. Then $b=\frac{15\times16}{12}=\frac{240}{12}=20$.

Answer:

$a = 25$
$b = 20$