SOLUTION: One leg of a right triangle is three times as long as the other. Write the lengthof the hypotenuse as a function of the shorter leg. a) c = (something i can't read)(square root

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Question 229995: One leg of a right triangle is three times as long as the other. Write the lengthof the hypotenuse as a function of the shorter leg.
a) c = (something i can't read)(square root of a)
b) c = 2a
c) c = (something i can't read)(square root of 10)
d) c = 10(a squared)
Answer by Earlsdon(6103) About Me  (Show Source):
You can put this solution on YOUR website!
Let a and b be the two legs of this triangle and c is the hypotenuse.
b+=+3a "One leg (b) is three times as long as the other (3a)."
Use the Pythagorean theorem.
c%5E2+=+a%5E2%2Bb%5E2 Substitute b+=+3a
c%5E2+=+a%5E2%2B%283a%29%5E2 Combine like-terms on the right side.
c%5E2+=+a%5E2%2B9a%5E2
c%5E2+=+10a%5E2 Take the square root of both sides.
c+=+sqrt%2810%29%2Aa or highlight%28c+=+a%2Asqrt%2810%29%29