In a right triangle with legs 6 and 8, what is the length of the hypotenuse?

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Multiple Choice

In a right triangle with legs 6 and 8, what is the length of the hypotenuse?

Explanation:
In any right triangle, the hypotenuse length comes from the Pythagorean theorem: the square of the hypotenuse equals the sum of the squares of the legs. With legs 6 and 8, the hypotenuse is sqrt(6^2 + 8^2) = sqrt(36 + 64) = sqrt(100) = 10. This also matches the familiar 3-4-5 triangle scaled by 2, giving 6-8-10. The other possibilities don’t fit the Pythagorean relation: 6 or 8 would be a leg, not the longest side, and 12 would not satisfy 6^2 + 8^2 = 12^2. So the hypotenuse length is 10.

In any right triangle, the hypotenuse length comes from the Pythagorean theorem: the square of the hypotenuse equals the sum of the squares of the legs. With legs 6 and 8, the hypotenuse is sqrt(6^2 + 8^2) = sqrt(36 + 64) = sqrt(100) = 10. This also matches the familiar 3-4-5 triangle scaled by 2, giving 6-8-10. The other possibilities don’t fit the Pythagorean relation: 6 or 8 would be a leg, not the longest side, and 12 would not satisfy 6^2 + 8^2 = 12^2. So the hypotenuse length is 10.

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