In a right triangle with legs 3 and 4, the hypotenuse is which value?

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Multiple Choice

In a right triangle with legs 3 and 4, the hypotenuse is which value?

Explanation:
In a right triangle, the square of the hypotenuse equals the sum of the squares of the legs. With legs 3 and 4, you get 3^2 + 4^2 = 9 + 16 = 25. The hypotenuse is the positive square root of that, so c = sqrt(25) = 5. This matches the well-known 3-4-5 triangle, where the longest side is 5. A hypotenuse must be longer than each leg, and 5 fits the Pythagorean relation for these legs; 3 or 4 wouldn’t satisfy the required sum, and 6 would not match 25.

In a right triangle, the square of the hypotenuse equals the sum of the squares of the legs. With legs 3 and 4, you get 3^2 + 4^2 = 9 + 16 = 25. The hypotenuse is the positive square root of that, so c = sqrt(25) = 5. This matches the well-known 3-4-5 triangle, where the longest side is 5. A hypotenuse must be longer than each leg, and 5 fits the Pythagorean relation for these legs; 3 or 4 wouldn’t satisfy the required sum, and 6 would not match 25.

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