Posted by Fabiola on .
A Norman window has the shape of a rectangle surmounted by a semicircle. (Thus the diameter of the semicircle is equal to the width of the rectangle.) If the perimeter of the window is 46 ft, find the dimensions of the window so that the greatest possible amount of light is admitted.
Enter your answers correct to two decimal places. Remember to take into account in your calculations that there is only half of a circle.
1.The length of the bottom of the rectangle is________ feet.
2.The length of each of the sides of the rectangle is ________feet.
I would let the bottom of the rectangle be 2x, that way you can let the radius of the circle be x, and avoid fractions.
Let the height of the rectangle by y.
Your main equation is
Area = xy = 1/2 Pi*x^2
but we know P=46
so 2x+2y + 1/2(2Pi*x) = 46
solve this for y, and substitute y in your Area equation
Differentiate,set equal to zero, and solve.