00:01
In this question we have given a rancher enclosed with two adjacent rectangular chorus that is given as follows.
00:11
Total fencing of the rancher is given to us is 200 feet.
00:27
And we have to find the dimension of each coral so that the area enclosed by this will be maximum.
00:35
Let width be x and this one.
00:40
Will be the height edge.
00:45
Now this width will be same for each four of them and the height will be same for each of three sides.
00:51
Now from the figure we have perimeter is equal to 4x plus 3y.
01:08
Let us first name is y.
01:10
So it implies 200 is equal to 4x plus 3y because we have given perimeter as 200.
01:17
So it implies y is equals to 200 divided by 3 minus 4 divided by 3 multiplied with x.
01:30
Let us name this as equation 1.
01:33
Now we know that area of a rectangle is given by width multiplied with 5.
01:47
So from the figure, here we have two enclosed corals.
01:55
So the total area will be two times of width multiplied with height.
02:01
So this is equals to 2 multiplied with x multiplied with y.
02:08
So it is equals to 2 multiplied with x.
02:11
Now substrate out the value of y, that is 200 divided by 3 minus 4 divided by 3 multiplied with x using equation.
02:22
So this is equals to 2x multiplied with 200 divided by 3...