Window area question, express as function of Area

[lovemake1]

1. The problem statement, all variables and given/known data

A window has the shape of a rectangle surmounted by an equilateral triangle. Given that the perimeter of the window is 15 feet, express the area as a function of the length of one side of the equilateral triangle.

2. Relevant equations

Area of an equaliteral triangle : x^2(sqrt (3)) / 4

Surface area of the window : 3x + 2y = 15
reduced to : y = (15 - 3x) / 2

Volume of the window: X^2(sqrt(3)) / 4 + xy

3. The attempt at a solution

y = (15 - 3x) / 2 has domain of 0 <= x <= 5

i subbed in y into the vlume of the window,
x^2(sqrt(3)) / 4 + x(15-3x)/2

and after factoring out the x, I got [x(x*Sqrt(3) - 6x + 30)] / 4
and with new domain 0 < x < 5.


Am i takin the right approach? am i suppose to leave the sqrt where it is right now?
please help

[hunt_mat]

Wouldn't the perimeter be 2x+2y=15? Then the area of the window is given by A=xy, but you know that x+y=7.5, then...

[Mentallic]

Wouldn't the perimeter be 2x+2y=15? Then the area of the window is given by A=xy, but you know that x+y=7.5, then...

No, you're missing the equilateral triangle.

Lovemake1 yes that's perfect.

[hunt_mat]

No, it says the perimeter of the 15, if the triangle fits snugly into the rectangle and the sides of the triangle is L, the one side is length L and the other side is given by L\sqrt{3}/2, so the area is given by L^{2}\sqrt{3}/2.

[Mentallic]

Surmounted means to sit on top of, not to sit snugly into.

And by the way, for an equilateral triangle, if one side is length L then the area is \frac{\sqrt{3}}{4}L^2

[hunt_mat]

Ah! I read surrounded.

[Mentallic]

Ah! I read surrounded.

That would make for a weird question :tongue:

[hunt_mat]

Not quite, it would mean that you could get a number for the area by using the perimeter.

Mat