SOLUTION: The lengths of the shortest side is 7 inches shorter than the middle side, while the longest side (hypotenuse) is 1 inch longer than the middle side. Find the lengths of the sides

Algebra ->  Customizable Word Problem Solvers  -> Misc -> SOLUTION: The lengths of the shortest side is 7 inches shorter than the middle side, while the longest side (hypotenuse) is 1 inch longer than the middle side. Find the lengths of the sides      Log On

Ad: Over 600 Algebra Word Problems at edhelper.com


    

Question 1146067: The lengths of the shortest side is 7 inches shorter than the middle side, while the longest side (hypotenuse) is 1 inch longer than the middle side. Find the lengths of the sides.
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let the length of the middle side = +x+ in.
The length of the shortest side = +x+-+7+ in.
The length of the hypotenuse = +x+%2B+1+ in.
-----------------------------------------------------
+x%5E2+%2B+%28+x-7+%29%5E2+=+%28+x+%2B+1+%29%5E2+
+x%5E2+%2B+x%5E2+-+14x+%2B+49+=+x%5E2+%2B+2x+%2B+1+
+x%5E2+-+16x+%2B+48+=+0+
+%28+x+-+4+%29%2A%28+x+-+12+%29+=+0+ ( by looking at it )
+x+=+4+
+x+=+12+
---------------------
I'll choose +x+=+4+
+x%5E2+%2B+%28+x-7+%29%5E2+=+%28+x+%2B+1+%29%5E2+
+4%5E2+%2B+%28+4-7+%29%5E2+=+%28+4+%2B+1+%29%5E2+
+16+%2B+9+=+25+
This doesn't work because you can't take 7 in from 4 in
--------------------------------
+x+=+12+
+x%5E2+%2B+%28+x-7+%29%5E2+=+%28+x+%2B+1+%29%5E2+
+12%5E2+%2B+%28+12-7+%29%5E2+=+%28+12+%2B+1+%29%5E2+
+144+%2B+25+=+169+
--------------------------------
5 - 12 - 13 are the sides