In a right triangle with legs 9 and 12, what is the length of the hypotenuse?

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Multiple Choice

In a right triangle with legs 9 and 12, what is the length of the hypotenuse?

Explanation:
In a right triangle, the square of the hypotenuse equals the sum of the squares of the legs. So for legs 9 and 12, compute 9^2 + 12^2 = 81 + 144 = 225. The hypotenuse is the square root of that sum, which is sqrt(225) = 15. So the hypotenuse length is 15. A longer number like 18 or 21 would require a different sum of squares, and 12 is one of the legs, not the hypotenuse, so it wouldn’t fit the relationship for these leg lengths.

In a right triangle, the square of the hypotenuse equals the sum of the squares of the legs. So for legs 9 and 12, compute 9^2 + 12^2 = 81 + 144 = 225. The hypotenuse is the square root of that sum, which is sqrt(225) = 15. So the hypotenuse length is 15. A longer number like 18 or 21 would require a different sum of squares, and 12 is one of the legs, not the hypotenuse, so it wouldn’t fit the relationship for these leg lengths.

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