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: Define the ratio of similarity

Let the hypotenuse of the smaller triangle be \( h_s = 5 \) inches and the hypotenuse of the larger triangle be \( h_l \). The ratio of the sides of the two similar triangles is \( 2:5 \), which means the ratio of their corresponding sides (including hypotenuses) is also \( 2:5 \). So we can set up a proportion: \( \frac{2}{5}=\frac{h_s}{h_l} \).

Step2: Solve for \( h_l \)

Substitute \( h_s = 5 \) into the proportion: \( \frac{2}{5}=\frac{5}{h_l} \). Cross - multiply to get \( 2\times h_l=5\times5 \), which simplifies to \( 2h_l = 25 \). Then divide both sides by 2: \( h_l=\frac{25}{2}=12.5 \).

Answer:

12.5 (corresponding to option e)