CBSE Class 12-science Answered
![question image](http://images.topperlearning.com/topper/new-ate/top_mob170332182012480729541241cbfa-58b1-4b13-95fd-835522fc9327.jpg)
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)
-------------------------------------------
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)
-------------------------------------------
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
Concept Videos
![](http://images.topperlearning.com/topper/questions/1205_image191.gif)