In a right triangle, the legs are in the ratio 3:4. What is the ratio of the hypotenuse to the shorter leg?

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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 right triangle, the legs are in the ratio 3:4. What is the ratio of the hypotenuse to the shorter leg?

Explanation:
When the legs are in the ratio 3:4, you can treat them as 3k and 4k for some positive number k. Using the Pythagorean theorem, the hypotenuse is sqrt((3k)^2 + (4k)^2) = sqrt(9k^2 + 16k^2) = sqrt(25k^2) = 5k. The shorter leg is 3k, so the ratio of the hypotenuse to the shorter leg is 5k : 3k, which simplifies to 5:3. This aligns with the 3-4-5 family of right triangles, where the hypotenuse is 5 when the shorter leg is 3.

When the legs are in the ratio 3:4, you can treat them as 3k and 4k for some positive number k. Using the Pythagorean theorem, the hypotenuse is sqrt((3k)^2 + (4k)^2) = sqrt(9k^2 + 16k^2) = sqrt(25k^2) = 5k. The shorter leg is 3k, so the ratio of the hypotenuse to the shorter leg is 5k : 3k, which simplifies to 5:3. This aligns with the 3-4-5 family of right triangles, where the hypotenuse is 5 when the shorter leg is 3.

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