The Pythagorean theorem: In a right triangle with legs 9 and 12, what is the hypotenuse?

The Pythagorean theorem: In a right triangle with legs 9 and 12, what is the hypotenuse?

• A. 9
• B. 12
• C. 15
• D. 21

Answer: (C)

In a right triangle, the longest side, the hypotenuse, satisfies the relation c^2 = a^2 + b^2, where a and b are the legs. Here the legs are 9 and 12, so the hypotenuse is sqrt(9^2 + 12^2) = sqrt(81 + 144) = sqrt(225) = 15. The numbers 9 and 12 are the legs, so they can’t be the hypotenuse; 21 wouldn’t fit the Pythagorean relation with these legs since 9^2 + 12^2 ≠ 21^2. Therefore, the hypotenuse is 15.

In a right triangle, the longest side, the hypotenuse, satisfies the relation c^2 = a^2 + b^2, where a and b are the legs. Here the legs are 9 and 12, so the hypotenuse is sqrt(9^2 + 12^2) = sqrt(81 + 144) = sqrt(225) = 15. The numbers 9 and 12 are the legs, so they can’t be the hypotenuse; 21 wouldn’t fit the Pythagorean relation with these legs since 9^2 + 12^2 ≠ 21^2. Therefore, the hypotenuse is 15.