Question

You are building a new double garage and use the length and width of your two cars to estimate the area needed. Your car measurements are Car 1: 14 ft. 2 in. by 5 ft. 7 in. Car 2: 14 ft. 6 in. by \(5 \mathrm{ft}\). 9 in. a. Based on these measurements, what would be a reasonable floor plan for your garage? Explain. b. What is the area of the floor plan you designed in part a?

Short answer

Answer: The approximate area of the garage floor plan is 283.66 square feet.

Step-by-step solution

Convert car dimensions to feet

We'll start by converting each car's length and width from feet and inches to only feet. To convert inches to feet, simply divide the number of inches by 12. Car 1 Length: 14 ft 2 in = 14 + (2/12) = 14.1667 ft Car 1 Width: 5 ft 7 in = 5 + (7/12) = 5.5833 ft Car 2 Length: 14 ft 6 in = 14 + (6/12) = 14.5 ft Car 2 Width: 5 ft 9 in = 5 + (9/12) = 5.75 ft

Determine a suitable floor plan

Now, we will decide on a floor plan for the garage that will accommodate both cars comfortably. A reasonable assumption would be to place the cars side by side, leaving some extra space between them and around the sides for easy movement. To accommodate both cars side by side, we can determine the total width of the garage by adding the width of both cars and some additional space. For example, we can add an extra 2 feet of space between the cars and an extra 1 foot on each side of the garage. Garage Width = Car 1 Width + Extra Space Between Cars + Car 2 Width + Extra Space on Both Sides Garage Width = 5.5833 ft + 2 ft + 5.75 ft + 2 ft = 15.3333 ft For the length of the garage, we can use the length of the longest car and add extra space at the front and back for easy movement. For example, we can add an extra 2 feet to the front and back of the garage. Garage Length = Longest Car Length + Extra Space to the front and back Garage Length = 14.5 ft + 4 ft = 18.5 ft

Calculate the area of the garage floor plan

Finally, we'll calculate the area of the floor plan based on the length and width determined in Step 2. The area of a rectangle can be calculated using the formula: Area = Length × Width Area = 18.5 ft × 15.3333 ft Area ≈ 283.66 ft^2 So, the area of the garage floor plan is approximately 283.66 square feet.