SOLUTION: the longer leg of a right triangle is 1 unit longer than the shorter leg. If the hypotenuse is 2 units longer than the shorter leg, find the lenghts of the sides of the triangle
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Question 802665: the longer leg of a right triangle is 1 unit longer than the shorter leg. If the hypotenuse is 2 units longer than the shorter leg, find the lenghts of the sides of the triangle Answer by Cromlix(4381) (Show Source):
You can put this solution on YOUR website! Shorter leg = x
Longer leg = 1 + x
Hypotenuse = 2 + x
x^2 + (1 + x)^2 = (2 + x)^2
x^2 + 1 + 2x + x^2 = 4 + 4x + x^2
collect like terms:
2x^2 + 2x + 1 = x^2 + 4x + 4
x^2 - 2x - 3 = 0
(x - 3)(x + 1) = 0
x + 1 = 0
x = -1 (no answer, x<0)
x - 3 = 0
x = 3
Shorter leg = 3 units
Longer leg = 4 units
Hypotenuse = 5 units
Hope this helps.
:-)
