SOLUTION: In a right triangle, the length of the longer leg is 7 more inches than the shorter leg. The length of the hypotenuse is 8 more inches than the length of the shorter leg a) If the

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Question 210200: In a right triangle, the length of the longer leg is 7 more inches than the shorter leg. The length of the hypotenuse is 8 more inches than the length of the shorter leg
a) If the shortest leg is represented by x, write expressions for the longer leg
and the hypotenuse in terms of x. Label them on the diagram.
(b) Write an equation using the Pythagorean Theorem that relates the three
sides together and solve it for the value of x.
(c) Find all three side lengths, and check your answer by verifying that
a^2 + b^2 = c^2 .

Answer by Earlsdon(6294) About Me  (Show Source):
You can put this solution on YOUR website!
a) Longer leg = x+7.
Hypotenuse = x+8.
b) %28x%2B8%29%5E2+=+x%5E2%2B%28x%2B7%29%5E2 Solve for x.
x%5E2%2B16x%2B64+=+x%5E2%2Bx%5E2%2B14x%2B49
x%5E2%2B16x%2B64+=+2x%5E2%2B14x%2B49 Subtract x%5E2 from both sides.
16x%2B64+=+x%5E2%2B14x%2B49 Subtract 16x from both sides.
64+=+x%5E2-2x%2B49 Subtract 64 from both sides.
0+=+x%5E2-2x-15
x%5E2-2x-15+=+0 Factor.
%28x%2B3%29%28x-5%29+=+0 so that...
x+=+-3 or highlight%28x+=+5%29 Discard the negative solution as length is a positive quantity.
c)
Hypotenuse is:
c+=+x%2B8
c+=+5%2B8
c+=+13
Longer side (a) is:
a+=+x%2B7
a+=+5%2B7
a+=+12
Shorter side (b) is:
b+=+x
b+=+5 Check:
c%5E2+=+a%5E2%2Bb%5E2
13%5E2+=+12%5E2%2B5%5E2
169+=+144%2B25
169+=+169 OK!