SOLUTION: in a right triangle the measure of the legs are 16 and x+10 and the measure of the hypotenuse is 2x-6 find the value of x

Algebra ->  Triangles -> SOLUTION: in a right triangle the measure of the legs are 16 and x+10 and the measure of the hypotenuse is 2x-6 find the value of x      Log On


   

Question 890770: in a right triangle the measure of the legs are 16 and x+10 and the measure of the hypotenuse is 2x-6 find the value of x
Answer by JulietG(1812) About Me  (Show Source):
You can put this solution on YOUR website!
a%5E2+b%5E2=c%5E2
16%5E2 + %28x%2B10%29%5E2 = %282x-6%29%5E2
256 + x%5E2+20x+100 = 4x%5E2-24x+36
Subtract x%5E2 from each side
356 + 20x = 3x%5E2-24x+36
Subtract 356 from each side, subtract 20x from each side
0 = 3x%5E2-44x-320
Factor
(3x+16)(x-20)
X must be a counting number so we can disregard the first factor.
x-20=0
x=20
.
Let's plug it in to see if it works.
a%5E2+b%5E2=c%5E2
Sides are 16, X=10 (20+10), hypotenuse 2x-6 (40-6)
16%5E2+30%5E2=34%5E2
256+900=1156
Success!