SOLUTION: In a right triangle ABC , measure of angle C=90 degrees. If AB=6x-1, BC=4x+6 and AC=2x+1, find x.

Algebra ->  Pythagorean-theorem -> SOLUTION: In a right triangle ABC , measure of angle C=90 degrees. If AB=6x-1, BC=4x+6 and AC=2x+1, find x.      Log On


   

Question 1072815: In a right triangle ABC , measure of angle C=90 degrees. If AB=6x-1, BC=4x+6 and AC=2x+1, find x.
Found 2 solutions by Fombitz, MaxWong:
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
AB%5E2=AC%5E2%2BBC%5E2
%286x-1%29%5E2=%282x%2B1%29%5E2%2B%284x%2B6%29%5E2
36x%5E2-12x%2B+1=4x%5E2%2B4x%2B+1+%2B+16x%5E2+%2B48x+%2B36
36x%5E2-12x%2B+1=+20x%5E2+%2B52x+%2B37
16x%5E2-64x-36=+0
4x%5E2-16x-9=+0
%282x-9%29%282x%2B1%29=0
Only positive x values make sense here,
2x-9=0
2x=9
x=9%2F2

Answer by MaxWong(38) About Me  (Show Source):
You can put this solution on YOUR website!
(2x+1)^2 + (4x+6)^2 = (6x-1)^2
4x^2 + 4x + 1 + 16x^2 + 48x + 36 = 36x^2 - 12x + 1
20x^2 + 52x + 37 = 36x^2 - 12x + 1
16x^2 - 64x - 36 = 0
x = %28-%28-64%29%2B-sqrt%2A%28%28-64%29%5E2-%284%29%2816%29%28-36%29%29%29%2F%282%2816%29%29=2%2B-5%2F2
x = 9/2 or -1/2(rejected)