Question 1171341
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   {{{(1/2)x*(2x+4)}}} = 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(1760)}}}  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 <U>ANSWER</U>:  the base of the triangle is  20 inches.
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Solved.


So, lazy person can solve it mentally . . .