SOLUTION: How do you find the value of x in a right triangle. The sides are 2x - 1; 3x; and x+7 for the perimeter

Algebra ->  Triangles -> SOLUTION: How do you find the value of x in a right triangle. The sides are 2x - 1; 3x; and x+7 for the perimeter      Log On


   

Question 953106: How do you find the value of x in a right triangle. The sides are 2x - 1; 3x; and x+7 for the perimeter
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!
use Pythagorean theorem:
if the sides are %282x-1%29,+3x, and %28x%2B7%29, and +3x is hypotenuse, then we have
+%283x%29%5E2=%282x-1%29%5E2%2B%28x%2B7%29%5E2........solve for x
+9x%5E2=4x%5E2-4x%2B1%2Bx%5E2%2B14x%2B49
+9x%5E2=5x%5E2%2B10x%2B50
+9x%5E2-5x%5E2-10x-50=0
+4x%5E2-10x-50=0...simplify
+2x%5E2-5x-25=0
+2x%5E2-10x%2B5x-25=0
+%282x%5E2-10x%29%2B%285x-25%29=0
+2x%28x-5%29%2B5%28x-5%29=0
+%282x%2B5%29%28x-5%29=0
if +%282x%2B5%29=0=>x=-5%2F2........disregard negative solution, side length cannot be negative
if +%28x-5%29=0=>x=5...our solution
now find sides length:
%282x-1%29=2%2A5-1=9
+3x=3%2A5=15
%28x%2B7%29=5%2B7=12
so, the perimeter is P=9%2B15%2B12=36