SOLUTION: I am havin such a hard time please help me? The length of one leg of a right triangle is 3 in. more than the other. If the length of the hypotenuse is 8 in., what are the lengths

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Question 80472: I am havin such a hard time please help me? The length of one leg of a right triangle is 3 in. more than the other. If the length of the hypotenuse is 8 in., what are the lengths of the two legs?
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
The length of one leg of a right triangle is 3 in. more than the other. If the length of the hypotenuse is 8 in., what are the lengths of the two legs?
:
Let the "other" leg = x:
:
It says:
"The length of one leg of a right triangle is 3 in. more than the other."
Therefore:
one leg = (x+3)
:
Given the hypotenuse = 8
:
Using pythag
x^2 + (x+3)^2 = 8^2
:
FOIL (x+3)(x+3)
x^2 + x^2 + 6x + 9 = 64
:
2x^2 + 6x + 9 - 64 = 0
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2x^2 + 6x - 55 = 0; a quadratic equation
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Will not readily factor so use the quadratic formula
a = 2; b = 6; c = -55
:
x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+
:
x+=+%28-6+%2B-+sqrt%28+6%5E2-4%2A2%2A-55+%29%29%2F%282%2A2%29+
:
x+=+%28-6+%2B-+sqrt%28+36+-+%28-440%29+%29%29%2F%284%29+
:
x+=+%28-6+%2B-+sqrt%28+36+%2B+440%29%29%2F%284%29+
:
x+=+%28-6+%2B-+sqrt%28476%29%29%2F%284%29+
:
Two solutions:
x+=+%28-6+-+21.87%29%2F4
x+=+-27.817%2F4%29
x = -6.954
and
x+=+%28-6+%2B+21.817%29%2F4
x+=+%2B15.817%2F4%29
x = +3.954, this will be our solution
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Of the course the other leg will be 3.954 + 3 = 6.954
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Easy to check this on a calc: enter
3.954^2 + 6.954^2 = 63.99 ~ 64 which is 8^2
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Think you can do this now, any questions?