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?

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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(39616)   (Show Source): You can put this solution on YOUR website!
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Answer by ikleyn(52776)   (Show Source): You can put this solution on YOUR website!
.

    = 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    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 . . .



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