A rectangular dog kennel is to be constructed alongside a house with 60m of fencing. If the house serves as one side of the kennel, determine the greatest possible area that can be enclosed.

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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.

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