SOLUTION: The longest side of a right angle triangle it’s one less than two times the length of the short side the remaining side is two units longer than the shorter side what are the dim

Algebra ->  Coordinate Systems and Linear Equations  -> Linear Equations and Systems Word Problems -> SOLUTION: The longest side of a right angle triangle it’s one less than two times the length of the short side the remaining side is two units longer than the shorter side what are the dim      Log On


   

Question 1173520: The longest side of a right angle triangle it’s one less than two times the length of the short side the remaining side is two units longer than the shorter side what are the dimensions of the triangle
Found 2 solutions by ikleyn, greenestamps:
Answer by ikleyn(52797) About Me  (Show Source):
Answer by greenestamps(13200) About Me  (Show Source):
You can put this solution on YOUR website!


The short side (leg) is x; the longest side (hypotenuse) is 2x-1; the other leg is x+2.

Use the Pythagorean Theorem....

x%5E2%2B%28x%2B2%29%5E2+=+%282x-1%29%5E2
x%5E2%2Bx%5E2%2B4x%2B4+=+4x%5E2-4x%2B1
0+=+2x%5E2-8x-3

No rational roots; use the quadratic formula with the positive root.



The leg lengths are
x = %284%2Bsqrt%2822%29%29%2F2
x+2 = %284%2Bsqrt%2822%29%29%2F2%2B2+=+%288%2Bsqrt%2822%29%29%2F2

The hypotenuse is
2x-1 = %284%2Bsqrt%2822%29%29-1+=+3%2Bsqrt%2822%29

CHECK:



%282x-1%29%5E2+=+9%2B6sqrt%2822%29%2B22+=+31%2B6sqrt%2822%29