Answer:
.
Step-by-step explanation:
Let x represent side of kennel opposite to house and y represent other sides.
We have been given that a rectangular dog kennel is to be constructed alongside a house with 60 m of fencing.
Since fencing will cover 3 sides of kennel, so perimeter of kennel would be:
Let us solve for x.
The area of the kennel would be product of its sides that is:
Now, we will substitute in area equation as:
Let us find the derivative as shown below:
Now, we will set derivative equal to 0 and solve for y.
Upon substituting in area function, we will greatest possible area.
Therefore, the greatest possible area that can be enclosed by 60 m of fencing is 450 square meters.