Question

the lengths of the corresponding sides of 2 similar right triangles are in the ratio of 2:5. if the hypotenuse of the smaller triangle is 5 inches long, how many inches long is the hypotenuse of the larger triangle? a 2 b 2.5 c 7 d 10 e 12.5

Explanation:

Step1: Set up the proportion

Let $x$ be the hypotenuse of the larger triangle. The ratio of the sides of the two similar right - triangles is $2:5$. We know that $\frac{\text{hypotenuse of smaller triangle}}{\text{hypotenuse of larger triangle}}=\frac{2}{5}$. Given the hypotenuse of the smaller triangle is 5 inches. So, $\frac{2}{5}=\frac{5}{x}$.

Step2: Cross - multiply

Cross - multiplying the proportion $\frac{2}{5}=\frac{5}{x}$ gives us $2x = 5\times5$.

Step3: Solve for $x$

We have $2x=25$, then $x=\frac{25}{2}=12.5$.

Answer:

E. 12.5