In a right triangle with legs 3 and 4, what is the length of the hypotenuse?

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Multiple Choice

In a right triangle with legs 3 and 4, 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. With legs of 3 and 4, the hypotenuse c satisfies c^2 = 3^2 + 4^2 = 9 + 16 = 25, so c = sqrt(25) = 5. This is the well-known 3-4-5 right triangle, where 5 is the longest side. The other numbers don’t fit the equation for these legs: sqrt(13) would come from different leg lengths, 4 is a leg length not the hypotenuse, and 7 is too large to satisfy the relation.

In a right triangle, the square of the hypotenuse equals the sum of the squares of the legs. With legs of 3 and 4, the hypotenuse c satisfies c^2 = 3^2 + 4^2 = 9 + 16 = 25, so c = sqrt(25) = 5. This is the well-known 3-4-5 right triangle, where 5 is the longest side. The other numbers don’t fit the equation for these legs: sqrt(13) would come from different leg lengths, 4 is a leg length not the hypotenuse, and 7 is too large to satisfy the relation.

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