
Bob A. answered 11/01/14
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20 Years Making Science and Maths Understandable and Interesting!
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.