Asked by Kendra
A slide is attached to the side of a tree house. The height of the tree house is 6 less than double the distance from the baswe of the tree to the base of the slide. The length of the slide is 3 more than the height of the tree house. Find the length of the slide.
Answers
Answered by
Reiny
I followed your description , got a right-angled triangle, used Pythagoras, and got
x^2 + (2x-6)^2 = (2x-3)^2
x^2 + 4x^2 - 24x + 36 = 4x^2 - 12x + 9
x^2 - 12x + 27 = 0
(x-9)(x-3) = 0
x = 9 or x = 3
if x = 3, the sides would be 3, 0 and 3, which does not make a "slide"
so we'll go with x = 9
if x=9 , the slide is 2x-3 = 2(9)-3 = 15
x^2 + (2x-6)^2 = (2x-3)^2
x^2 + 4x^2 - 24x + 36 = 4x^2 - 12x + 9
x^2 - 12x + 27 = 0
(x-9)(x-3) = 0
x = 9 or x = 3
if x = 3, the sides would be 3, 0 and 3, which does not make a "slide"
so we'll go with x = 9
if x=9 , the slide is 2x-3 = 2(9)-3 = 15
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