SOLUTION: the legs of a right triangle are (x) and (x+2). The hypotenuse is (x+4). Find the length of each side of the triangle.

Algebra ->  Equations -> SOLUTION: the legs of a right triangle are (x) and (x+2). The hypotenuse is (x+4). Find the length of each side of the triangle.      Log On


   

Question 774214: the legs of a right triangle are (x) and (x+2). The hypotenuse is (x+4). Find the length of each side of the triangle.
Answer by ramkikk66(644) About Me  (Show Source):
You can put this solution on YOUR website!
Since it is a right triangle, we can apply the Pythagoras theorem
Square of hypotenuse = square of leg1 + square of leg2.
%28x+%2B+4%29%5E2+=+x%5E2+%2B+%28x+%2B+2%29%5E2
Expanding the Left and right sides
x%5E2+%2B+8%2Ax+%2B+16+=+x%5E2+%2B+x%5E2+%2B+4%2Ax+%2B+4+=+2%2Ax%5E2+%2B+4%2Ax+%2B+4
Moving all terms to one side
2%2Ax%5E2+-+x%5E2+%2B+4%2Ax+-+8%2Ax+%2B+4+-+16+=+0
x%5E2+-+4%2Ax+-+12+=+0
This is a standard quadratic equation which can b solved by factorization
x%5E2+-+6%2Ax+%2B+2%2Ax+-+12+=+0
x%2A%28x+-+6%29+%2B+2%2A%28x+-+6%29+=+0
%28x+%2B+2%29%2A%28x+-+6%29+=+0
The two roots (solutions) for x are
x + 2 = 0 or x = -2
x - 6 = 0 or x = 6
Take only the positive value of the x.
So one leg of the triangle is 6
The other leg is (6 + 2) or 8.
The hypotenuse is (6 + 4) or 10.
The sides of the triangle are 6, 8 and 10 units.
Hope you got it :)