SOLUTION: The hypotenuse of a right triangle is 6 units longer than the shorter leg. The longer side is 3 units more than the shorter side. Find the length of the shorter side.
Question 293338: The hypotenuse of a right triangle is 6 units longer than the shorter leg. The longer side is 3 units more than the shorter side. Find the length of the shorter side. Answer by ankor@dixie-net.com(22740) (Show Source):
You can put this solution on YOUR website! The hypotenuse of a right triangle is 6 units longer than the shorter leg.
The longer side is 3 units more than the shorter side.
Find the length of the shorter side.
:
Using pythag: a^2 + b^2 = c^2
:
let x = the shorter leg (a)
then
(x+3) = the longer leg (b)
and
(x+6) = the hypotenuse
:
x^2 + (x+3)^2 = (x+6)^2
FOIL
x^2 + (x^2 + 6x + 9) = x^2 + 12x + 36
Combine like terms on the left
x^2 + x^2 - x^2 + 6x - 12x + 9 - 36 = 0
A quadratic equation
x^2 - 6x - 27 = 0
Factors to
(x - 9)(x + 3) = 0
positive solutions
x = 9 units is the shorter side
then
9 + 3 = 12 units the longer side
and
9 + 6 = 15 units of the hypotenuse
;
:
Check solution
9^2 + 12^2 = 15^2
81 + 144 = 225
