SOLUTION: The area of a triangle is 126cm^2, and the altitude is 3 less than twice the base. Find the length of the base.

Question 176691: The area of a triangle is 126cm^2, and the altitude is 3 less than twice the base. Find the length of the base.
Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!
The area of a triangle is given by . Let the measure of the base be , then we are given that the altitude is , so and we are given that the area of this particular triangle is 126 square centimeters. Therefore:

Solve the quadratic by ordinary means. You can factor, complete the square, or use the quadratic formula -- all three methods work. You will get two roots as you should expect, except that one of them will be < 0. This absurd result for the measure of a side of a triangle is an extraneous root caused by squaring the variable in the process of solving the problem. Exclude the negative root. The positive root is your answer.

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