00:01
In this problem, we are provided with the following figure, which represents a coral that needs to be fenced.
00:10
We are also provided with 180 feet of fencing material.
00:21
So, in this question, we are asked to find out the dimensions that is, the value of x and y, such that the area of this coral is maximum.
00:35
By symmetry, we have these sides to also be equal to x and these sides to also be equal to y.
00:48
So now since the fencing is to be provided for the perimeter, we have 4x plus 3y y to be equal to 180 feet.
01:00
And now solving for y, we obtain y equals to 60 minus 4 over 3 .3.
01:07
3 times x.
01:09
Next, since we need to calculate the area, let us find an expression for the area a.
01:15
So the area a over here equals to the length times the breadth.
01:23
So here the length is 2x and the breadth is y...