Answer :

Let the radius of semicircle, length and breadth of rectangle be r, x and y respectively

AE = r

AB = x = 2r (semicircle is mounted over rectangle) …1

AD = y

**Given:** Perimeter of window = 10 m

x + 2y + πr = 10

2r + 2y + πr = 10

2y = 10 – (π + 2).r

y = … 2

To admit maximum amount of light, area of window should be maximum

Assuming area of window as A

A = xy +

A = (2r) () +

A = 10r - πr^{2} – 2r^{2} +

A = 10r – 2r^{2} -

Condition for maxima and minima is

10 – 4r - πr = 0

= - 4 - π < 0

For r = A will be maximum.

Length of rectangular part = (from equation 1)

Breath of rectangular part = (from equation 2)

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