SOLUTION: the legs of a right triangle have lengths x+4 and x+7. The hypotenuse has length 3x. Find the perimeter of the triangle

Algebra ->  Triangles -> SOLUTION: the legs of a right triangle have lengths x+4 and x+7. The hypotenuse has length 3x. Find the perimeter of the triangle      Log On


   

Question 451434: the legs of a right triangle have lengths x+4 and x+7. The hypotenuse has length 3x. Find the perimeter of the triangle
Answer by robertb(5830) About Me  (Show Source):
You can put this solution on YOUR website!
using the Pythagorean theorem, we get %28x%2B4%29%5E2+%2B+%28x%2B7%29%5E2+=+%283x%29%5E2
<==> x%5E2+%2B+8x+%2B+16+%2B+x%5E2+%2B+14x+%2B+49+=+9x%5E2
<==> 7x%5E2+-22x+-+65+=+0
<==> (7x + 13)(x-5) = 0
==> x = 5
The perimeter is x+4 +x+7 + 3x = 5x + 11
Hence the perimeter is 5*5 + 11 = 25 + 11 = 36.
(We cannot accept the other x-value -13/7 for an apparent reason.)