Bob A. answered • 11/01/14

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For a rectangle the perimeter is 2H + 2W (H and W being the height and width).

For a circle the Perimeter (Circumference) is Pi•D.

For this window the D is equal to the W of the rectangle

and the rectangular part has only 3 sides

and the circular part is 1/2 the circumference of the circle.

So the total perimeter of the window is

2H + W + (Pi•W)/2 = 742 cm

This is one equation.

The area of the rectangle part is = H•W

The area of the semi-circle is = 1/2 [Pi r^2] = 1/2 [Pi•(W/2)^2]

The total area is then:

H•W + 1/2 [Pi•(W/2)^2] = Amax

This is the other equation.

Two equations, two unknowns, H & W

Solve the first for H in terms of W

Plug that H into the second equation

(as if you were solving by substitution)

Then solve the second for the value that gives the largest area.