CBSE Class 12-science Answered

Perimeter = CA+ length of semi-circle arc AB + BD + DC

Perimeter = 2y + π x + 2y + 2x = (2 + π ) x + 4y

Since perimeter equals 10 , relation between x and y is

(2 + π ) x + 4y = 10 .............................(1)

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Area of window = area of rectangle ABCD + semicircle with diameter BC

Area of window, A  = (2x) (2y) + (π/2) x² =  4xy + (π/2) x² .................... (1)

From eqn.(1) , we get ,  4y = 10 - (2 + π ) x

Substituting 4y from above expression, we get from eqn.(1) as

A = 10x - [ 2 + (π /2 ) ] x²   ...........................(2)

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To get maximum area by adjusting the value of x , we differentiate eqn.(2) and equate it to zero

from above expression , we get x for maximum area as

x = 1.4 m