SOLUTION: The base of a triangle is 4 inches more than twice its height. If the area of the triangle is 440 square inches, what is the base of the triangle in inches?

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equation Customizable Word Problems -> SOLUTION: The base of a triangle is 4 inches more than twice its height. If the area of the triangle is 440 square inches, what is the base of the triangle in inches?      Log On


   

Question 1171340: The base of a triangle is 4 inches more than twice its height.
If the area of the triangle is 440 square inches, what is the base of the triangle in inches?
Found 2 solutions by josgarithmetic, ikleyn:
Answer by josgarithmetic(39615) About Me  (Show Source):
Answer by ikleyn(52765) About Me  (Show Source):
You can put this solution on YOUR website!
.

   %281%2F2%29x%2A%282x%2B4%29 = 440.


With my magic lamp, I will show you how to solve it mentally.


Multiply by 2 both sides


    x*(2x+4) = 880.


Multiply by 2 both sides ONE MORE TIME.  You will get


    2x*(2x+4) = 1760.


Now find MENTALLY (= guess) decomposition of the number 1760 into product of two factors, that differ by 4.


To faculitate guessing, recall that  sqrt%281760%29  is about 40, or slightly more than 40.


Taking it into account, you find this decomposition in 1 second


    1760 = 40*44.


Thus 2x = 40,  x = 40/2 = 20.


It is your ANSWER:  the base of the triangle is  20 inches.

Solved.

So, lazy person can solve it mentally . . .