SOLUTION: isosceles ghi has gh congruent to gi. gh is x^2, gi is -2x plus 15 and hi is -x plus 4 find the side lenghts

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Question 1096449: isosceles ghi has gh congruent to gi. gh is x^2, gi is -2x plus 15 and hi is -x plus 4 find the side lenghts
Answer by greenestamps(13203) About Me  (Show Source):
You can put this solution on YOUR website!

GH is the same length as GI:
x%5E2+=+-2x%2B15
x%5E2%2B2x-15+=+0
%28x%2B5%29%28x-3%29+=+0

The potential solutions are x=-5 and x=3; but we need to check to see if they make sense in the actual problem.

x = -5: GH = x^2 = (-5)^2 = 25; GI = -2x+15 = 10+15 = 25; HI is -x+4 = 5+4 = 9.
That works; the side lengths are 25, 25, and 9.

x = 3: GH = x^2 = 3^2 = 9; GI = -2x+15 = -6+15 = 9; HI = -x+4 = 1.
That also works: the side lengths are 9, 9, and 1.

So there are two different isosceles triangles that satisfy the given conditions.