SOLUTION: the hypotenuse of a right angled triangle is 6m more than twice the shortest side. If the third side is 2m less than the hypotenuse, find the sides of the triangle.
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Question 528751: the hypotenuse of a right angled triangle is 6m more than twice the shortest side. If the third side is 2m less than the hypotenuse, find the sides of the triangle. Answer by nerdybill(7384) (Show Source):
You can put this solution on YOUR website! the hypotenuse of a right angled triangle is 6m more than twice the shortest side. If the third side is 2m less than the hypotenuse, find the sides of the triangle.
Let x = shortest side
then
2x+6 = hypotenuse
2x+6-2 = 2x+4 = long side
.
x^2 + (2x+4)^2 = (2x+6)^2
x^2 + (2x+4)(2x+4) = (2x+6)(2x+6)
x^2 + 4x^2+16x+16 = 4x^2+24x+36
5x^2+16x+16 = 4x^2+24x+36
x^2+16x+16 = 24x+36
x^2-8x+16 = 36
x^2-8x-20 = 0
(x-10)(x+2) = 0
x {-2, 10}
throw out the negative solution leaving:
x = 10m (short side)
.
hypotenuse:
2x+6 = 2(10)+6 = 20+6 = 26m
.
long side:
2x+4 = 2(10)+4 = 20+4 = 24m
