In a certain right triangle, the sum of the lengths of the

yep, is one of the typical right triangles

13-12-5

so

26-24-10

A it is...

tried a few choices...wasnt getting the right answer, then, picked one of the famous triangles, 3-4-5 that didnt work, 5-12-13...works fine...

Thats correct guys, OA is A

Here is the detailed explanation:
The Pythagorean theorem states that the sum of the squares of the lengths of the legs of a triangle is equal to the square of the length of the hypotenuse.

Let A and B be the lengths of the sides. Let C be the length of the hypotenuse. Thus, we can set up the following equation:

A2 + B2 = C2

We are told that the sum of the legs and hypotenuse is 60 inches. We are also told that the hypotenuse is 26 inches. Thus, we can set up the following equation:

A + B + 26 = 60
A + B = 34
A = 34 - B

Plugging the value of A and C into the first equation:

(34 - B)2 + B2 = 262
(34 - B)(34 - B) + B2 = 676
1156 - 68B + B2 + B2 = 676
2B2 - 68B + 1156 = 676
2B2 - 68B + 480 = 0
(2B - 48)(B - 10) = 0
B = 10 or B = 24