SOLUTION: Find the base of a triangle with an area of 8 square meters if the altitude of the triangle is 6 meters less than the base

Question 889962: Find the base of a triangle with an area of 8 square meters if the altitude of the triangle is 6 meters less than the base

Answer by harpazo(655) (Show Source): You can put this solution on YOUR website!
A = 1/2 times base times height
Let b = base
8 = 1/2 times b times b - 6
8 = (b/2)(b-6)
8 = (b^2-6b)/2
8 * 2 = b^2-6b
16 = b^2-6b
b^2 -6b - 16 = 0
Solve the quadratic equation for b to find your answer.
(b - 8)(8 + 2) = 0

Set each factor to zero and solve for b individually.
b - 8 = 0
b = 8
b + 2 = 0
b = -2
Reject b = -2 because distance cannot be NEGATIVE.
Answer: Base = 8 meters.

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