SOLUTION: The area of a triangle is 56ft^2. If the base is 9 ft more than the altitude, find the length of the base and the altitude.

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Question 166039: The area of a triangle is 56ft^2. If the base is 9 ft more than the altitude, find the length of the base and the altitude.
Answer by orca(409) About Me  (Show Source):
You can put this solution on YOUR website!
Let x be the altitude, then the base is x + 9.
Its area is %281%2F2%29%2Ax%28x%2B9%29
As its area is 56, we have
%281%2F2%29%2Ax%28x%2B9%29=56
Solving for x, we have
x%28x%2B9%29=112
x%5E2%2B9x=112
x%5E2%2B9x-112=0
x+=+%28-9+%2B-+sqrt%28+9%5E2-4%2A1%2A%28-112%29+%29%29%2F%282%2A1%29+
x+=+%28-9+%2B-+sqrt%28+529+%29%29%2F2+
x+=+%28-9+%2B-+23%29%2F2+
So
x+=+%28-9+%2B+23%29%2F2=7+
Or
x+=+%28-9+-+23%29%2F2=-16 (reject this negative root)
Thus the length of the altitude is 7, and the length of the base is x+9 = 7+9=16.