Anorman window is constructed by adjoining a semicircle to the top of an ordinary rectangular window. find the dimensions of a norman window of maximum area when the total perimeter is 16 feet.

The maximum area of the window has a semicircle with diameter 4.48 ft and the length of the rectangle is 2.24 ft.

Let x represent the radius of the semicircle, hence the width of the rectangle = 2x. Also, the length of the rectangle is y

The perimeter of the window = πx + 2y + 2x = x(π + 2) + 2y

16 = x(π + 2) + 2y

The area of the window (A) = 0.5πx² + 2yx

Hence the maximum area of the window has a semicircle with diameter 4.48 ft and the length of the rectangle is 2.24 ft.

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Step-by-step explanation:

Given Perimeter of window

Suppose x and y be the dimension of rectangular window

Perimeter of rectangular portion

Perimeter of semicircle

so

Area of the window is

differentiate A w.r.t x to get maximum or minimum value

put to get maxima/minima

thus

for ,

x = 25/2304

step-by-step explanation:

b.an increase in a causes b to decrease