Question

120 side of building a veterinary clinic plans to build four identical dog kennels along the side of its building using 210 feet of fencing, as shown in the diagram. what should the dimensions of each kennel be to maximize the total enclosed area if no fencing is needed along the side of the building?

Answer 1

To maximize the total enclosed area, each kennel should have a length of 26.25 feet and width of 26.25 feet.

Step-by-step explanation:

To determine the dimensions of each kennel that will maximize the total enclosed area, we need to divide the available fencing into four equal parts. Since there are four kennels, each kennel will have 210/4 = 52.5 feet of fencing.

Let's assume the length of each kennel is x feet. Since the fencing is on the outside of the kennels, we will have to subtract the length of the kennel from the total enclosure length. So the width of each kennel will be (52.5 - x) feet.

The total enclosed area of each kennel is given by the formula: Area = Length x Width. Substituting the values, we get: (x)(52.5 - x) = 52.5x - x^2. To maximize this area, we need to find the maximum of the quadratic expression.

The maximum value of the quadratic expression occurs when x = 26.25 feet. Therefore, the dimensions of each kennel that will maximize the total enclosed area are: Length = 26.25 feet and Width = 26.25 feet.