- #1

lovemake1

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## Homework Statement

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.

## Homework 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

## 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