Question

I know that this question has been ask, but I'm confused.

Question:
"A rectangle is topped by an equilateral triangle, the sides of which are equal to the width of the rectangle. Find the maximum area of the window if the perimeter is 500 cm."

how does x(500-3x)/2 + √3/4 x^2 = (√3-6)/4 x^2 + 250x?

Answer 1

just expand it out

x(500-3x)/2 = -3/2 x^2 + 250x
so that gives the sum as
√3/4 x^2 - 3/2 x^2 + 250x
(√3/4 - 3/2) x^2 + 250x
(√3 - 6)/4 x^2 + 250x