A dog kennel owner needs to build a dog run (rectangular area) adjacent to a kennel cage (so that it is in the shape of a rectangle, but only three sides need to be built- one long side is already there). The short side walls of the run are to be cinder block (costs $0.50 per square foot) and the outer walls are to be chain link fence ($2.75 per square foot). Local regulations require the walls to be at least seven feet high and the are to measure no fewer than 120 square feet.

Question

A dog kennel owner needs to build a dog run (rectangular area) adjacent to a kennel cage (so that it is in the shape of a rectangle, but only three sides need to be built- one long side is already there). The short side walls of the run are to be cinder block (costs $0.50 per square foot) and the outer walls are to be chain link fence ($2.75 per square foot). Local regulations require the walls to be at least seven feet high and the are to measure no fewer than 120 square feet.

Any help would be greatly appericiated!

Answer 1

To determine the dimensions and cost of the dog run, we need to consider the minimum area required, the required height, and the cost of the materials.

Let's start by calculating the minimum area required for the dog run. The area of a rectangle is calculated by multiplying its length by its width. In this case, the long side is already there, so we only need to find the length of the short side.

Let's assume the length of the long side (adjacent to the kennel cage) is "L" feet. Since the area should be a minimum of 120 square feet, we can form an equation:

Area = Length × Width
120 = L × Width

Next, let's consider the height requirement stated in the local regulations. The walls should be at least seven feet high. Since there are three walls, the height of the dog run will be 7 feet.

Now, let's calculate the width of the dog run using the provided information:

Width = Area / Length
Width = 120 / L

To calculate the cost of the cinder block walls, we consider that the short sides of the dog run are made of cinder block, which costs $0.50 per square foot. The cost for the cinder block walls is given by:

Cost of Cinder Block Walls = Width × Height × Cost per square foot

Similarly, to calculate the cost of the chain link fence that forms the outer walls of the dog run, which costs $2.75 per square foot, we use the following formula:

Cost of Chain Link Fence = (Long Side + 2 × Width) × Height × Cost per square foot

By substituting the calculated values, we can find the total cost of the dog run.

Please provide the length (in feet) of the long side of the dog run so that we can calculate the dimensions and costs for you.