SOLUTION: A window is to be constructed in the shape of an equilateral triangle on top of a rectangle. If its perimeter is to be 600 cm, what is the maximum possible area of the window?

Algebra ->  Test -> SOLUTION: A window is to be constructed in the shape of an equilateral triangle on top of a rectangle. If its perimeter is to be 600 cm, what is the maximum possible area of the window?      Log On


   

Question 1093820: A window is to be constructed in the shape of an equilateral triangle on top of a rectangle. If its perimeter is to be 600 cm, what is the maximum possible area of the window?
Found 2 solutions by josgarithmetic, greenestamps:
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
(Actually drawing the figure would help.)

Take 2x as rectangle length and y as height of just the rectangle.
Each side of the triangle is also 2x (only two of them being sides for the window).

Perimeter, 600=6x%2B2y
y=300-3x
-
Total area, 2xy%2Bx%5E2%2Asqrt%283%29,...adjusted...
Total area, A=2x%28300-3x%29%2Bsqrt%283%29x%5E2, a quadratic function A
.
A=sqrt%283%29x%5E2%2B2x%28300-3x%29
A=sqrt%283%29x%5E2%2B600x-6x%5E2
A=%28sqrt%283%29-6%29x%5E2%2B600x
.
.
Maximum area will occur for 2%28sqrt%283%29-6%29x%2B600=0
or for
highlight_green%28%28sqrt%283%29-6%29x%2B300=0%29


Answer by greenestamps(13198) About Me  (Show Source):
You can put this solution on YOUR website!

note to josgarithmetic...

nice choice to let the side of the triangle be 2x instead of x, to avoid fractions.

But in the final stages of your response you used x instead of 2x as that length. You might want to edit your response