SOLUTION: One leg of a right triangle is half as long as the other. What is the length of the hypotenuse as a function of the shorter leg?

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Question 222839: One leg of a right triangle is half as long as the other. What is the length of the hypotenuse as a function of the shorter leg?
Answer by drj(1380) About Me  (Show Source):
You can put this solution on YOUR website!
One leg of a right triangle is half as long as the other. What is the length of the hypotenuse as a function of the shorter leg?

Step 1. Let x be the shorter leg and 2x be the other leg.

Step 2. To solve this problem, use the Pythagorean Theorem given as the sum of the squares of the legs is equal to the square of the hypotenuse c.

Step 3. Then,

c%5E2=x%5E2%2B%282x%29%5E2

c%5E2=x%5E2%2B4x%5E2

c%5E2=5x%5E2

Take the square root to both sides of the equation

c=x%2Asqrt%285%29

Step 3. ANSWER: The hypotenuse is x%2Asqrt%285%29 where x is the shorter leg.

I hope the above steps were helpful.

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Good luck in your studies!

Respectfully,
Dr J