Question

In a right triangle with legs measuring 2.5 inches and 3.5 inches, which of the following could be the lengths of the legs of a second triangle that is proportional to the first?

A. 10 in and 14 in
B. 5.5 in and 8.5 in
C. 7.5 in and 10.5 in
D. 3 in and 4.2 in

Answer 1

The lengths of the legs of the second triangle must be proportional to the lengths of the legs of the first triangle. We can set up a proportion and solve for the lengths of the second triangle's legs.

Step-by-step explanation:

The lengths of the legs of the second triangle must be proportional to the lengths of the legs of the first triangle. The ratio of the lengths of the corresponding sides of two similar triangles is equal to the ratio of their corresponding sides. So, we can set up a proportion using the given lengths and the lengths of the second triangle's legs:

2.5/3.5 = x/10

Cross multiply and solve for x:

2.5 * 10 = 3.5 * x

25 = 3.5x

x = 25/3.5 = 7.1429

Therefore, the lengths of the second triangle's legs could be approximately 7.14 inches and 10 inches. So, the answer is C. 7.5 in and 10.5 in.