SOLUTION: Suppose you need to construct a right triangle in which the shortest side is eight feet less than the largest side and the third side is seven feet more than the shortest side.

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Question 205479: Suppose you need to construct a right triangle in which the shortest side is eight feet less than the largest side and the third side is seven feet more than the shortest side.
Answer by Edwin McCravy(20055) About Me  (Show Source):
You can put this solution on YOUR website!
Suppose you need to construct a right triangle in which the shortest side is eight feet less than the largest side and the third side is seven feet more than the shortest side.

Smallest+=+Longest+-+8
Middle+=+Smallest+%2B+7
Smallest%5E2+%2B+Middle%5E2+=+Longest%5E2

system%28S=L-8%2CM=S%2B7%2CS%5E2%2BM%5E2=L%5E2%29

Substitute L-8 for S in M=S%2B7

M=S%2B7
M=%28L-8%29%2B7
M=L-8%2B7
M=L-1

Substitute L-8 for S and L-1 for M in S%5E2%2BM%5E2=L%5E2

S%5E2%2BM%5E2=L%5E2
%28L-8%29%5E2%2B%28L-1%29%5E2=L%5E2
%28L-8%29%28L-8%29%2B%28L-1%29%28L-1%29=L%5E2
%28L%5E2-8L-8L%2B64%29%2B%28L%5E2-L-L%2B1%29=L%5E2
%28L%5E2-16L%2B64%29%2B%28L%5E2-2L%2B1%29=L%5E2
L%5E2-16L%2B64%2BL%5E2-2L%2B1=L%5E2
2L%5E2-18L%2B65=L%5E2
L%5E2-18L%2B65=0
%28L-13%29%28L-5%29=0
L-13=0   L-5=0
   L=13    L=5

So the longest side is 13 ft or 5 ft
But we must check:

Substituting L=13   

Smallest+=+Longest+-+8+=+13-8=5
Middle+=+Smallest+%2B+7=5%2B7=12

That's one solution. Longest = 13 ft, Middle = 12 ft, Longest = 13 ft.

Substituting L=5   

Smallest+=+Longest+-+8+=+5-8=-3
Middle+=+Smallest+%2B+7=-3%2B7=4

That would require a triangle to have a negative side,
so we discard that as a solution.

Edwin