Question 1013551: In right triangle ABC, AC = x, BC = x + 1, and hypotenuse AB = 2x - 1. Find the length of AC only. [only an algebraic solution will be accepted]
Answer by ankor@dixie-net.com(22740)   (Show Source):
You can put this solution on YOUR website! In right triangle ABC, AC = x, BC = x + 1, and hypotenuse AB = 2x - 1.
Find the length of AC only.
:'
Using pythag a^2 + b^2 = c^2, where
a = x, which is AC
b = (x+1), which is BC
c = (2x-1), which is the hypotenuse AB
:
x^2 + (x+1)^2 = (2x-1)^2
FOIL
x^2 + (x^2 + 2x + 1) = 4x^2 - 4x + 1
combine like terms on the left
x^2 + x^2 - 4x^2 + 2x + 4x + 1 - 1 = 0
-2x^2 + 6x = 0
Factor out -2x
-2x(x - 3) = 0
resulting in
-2x = 0
and
x = +3, which is AC
:
:
See if that works, a=3, b=4, c=5
3^2 + 4^2 = 5^2
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