In a 3-4-5 right triangle, what is the square of the hypotenuse?

In a 3-4-5 right triangle, what is the square of the hypotenuse?

• A. 9
• B. 16
• C. 25
• D. 20

Answer: (C)

In a right triangle, the square of the hypotenuse equals the sum of the squares of the two legs. For a 3-4-5 triangle, the legs are 3 and 4, so compute 3^2 + 4^2 = 9 + 16 = 25. Therefore, the square of the hypotenuse is 25 (the hypotenuse itself is 5). The other numbers are just the squares of the legs (9 and 16); 20 doesn’t match the sum of the squares of the legs, so it can’t be the hypotenuse squared.

In a right triangle, the square of the hypotenuse equals the sum of the squares of the two legs. For a 3-4-5 triangle, the legs are 3 and 4, so compute 3^2 + 4^2 = 9 + 16 = 25. Therefore, the square of the hypotenuse is 25 (the hypotenuse itself is 5). The other numbers are just the squares of the legs (9 and 16); 20 doesn’t match the sum of the squares of the legs, so it can’t be the hypotenuse squared.