SOLUTION: The base of a triangle is 1 inch more than 3 times the height. If the area of the triangle is 40 square inches, then find the height.

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Question 1170835: The base of a triangle is 1 inch more than 3 times the height. If the area of the triangle is 40 square inches, then find the height.
Answer by ikleyn(52781) About Me  (Show Source):
You can put this solution on YOUR website!
.

Let x be the height, in inches.


Then the base is 3x+1  inch.


The area of the triangle is  %281%2F2%29%2Ax%2A%283x%2B1%29;   THEREFORE, your base equation is


    %281%2F2%29%2Ax%2A%283x%2B1%29 = 40   square inches.


Then you simplify it


    x*(3x+1) = 80

    3x^2 + x - 80 = 0


and solve it using the quadratic formula


    x%5B1%2C2%5D = %28-1+%2B-+sqrt%281+%2B+4%2A3%2A80%29%29%2F%282%2A3%29 = %28-1+%2B-+sqrt%28961%29%29%2F6.


You have two roots  %28-1%2B31%29%2F6 = 5  and  %28-1-31%29%2F6,  but only positive root is good as the solution to the problem.


ANSWER.  The height of the triangle is 5 inches.

Solved.