In a 3-4-5 right triangle, what is the length of the hypotenuse?

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Prepare for the AMSOC 26-003 Module A Test. Utilize flashcards and multiple choice questions with hints and explanations. Ace your exam!

Multiple Choice

In a 3-4-5 right triangle, what is the length of the hypotenuse?

Explanation:
The main concept is the Pythagorean theorem: in a right triangle, the square of the hypotenuse equals the sum of the squares of the two legs. Here, with legs 3 and 4, the hypotenuse length is sqrt(3^2 + 4^2) = sqrt(9 + 16) = sqrt(25) = 5. The hypotenuse is the longest side, opposite the right angle, so 5 is the correct length. The other options correspond to either a leg length or a different triangle (for example, sqrt(13) would come from legs 2 and 3), not this one.

The main concept is the Pythagorean theorem: in a right triangle, the square of the hypotenuse equals the sum of the squares of the two legs. Here, with legs 3 and 4, the hypotenuse length is sqrt(3^2 + 4^2) = sqrt(9 + 16) = sqrt(25) = 5. The hypotenuse is the longest side, opposite the right angle, so 5 is the correct length. The other options correspond to either a leg length or a different triangle (for example, sqrt(13) would come from legs 2 and 3), not this one.

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