SOLUTION: The longest side of a right triangle is 3 less than 4 times the shortest side. The third side measures 24 inches. Find the length of the shortest side.

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Question 844101: The longest side of a right triangle is 3 less than 4 times the shortest side. The third side measures 24 inches. Find the length of the shortest side.
Answer by lwsshak3(11628) About Me  (Show Source):
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The longest side of a right triangle is 3 less than 4 times the shortest side. The third side measures 24 inches. Find the length of the shortest side.
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let x= shortest side
4x-3= longest side=hypotenuse
by the pythagorean theorem
x^2+24^=(4x-3)^2
x^2+576=16x^2-24x+9
15x^2-24x-567=0
solve for x by quadratic formula:
x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+
a=15, b=-24, c=567
ans:
x=-27/5 (reject)
or
x=7
length of the shortest side=7
check:
x^2+24^2=49+576=625 (sum of sides squared)
(4x-3)^2=25^2=625 (hypotenuse squared)