Question

Josh just finished building a house for his dog. Now he wants to put carpet on the floor of the doghouse to keep him pet warm during the cold winter months ahead. Josh measured the perimeter of the floor at 122 inches. Use this information to answer the following questions. Show your work under each question. 1. If the width measurement of the floor is 25 inches, how many square feet of carpet does josh need to cover the entire floor?. 2. If carpet costs $12.00 a square foot, how much will josh have to spend?

Answer 1

To determine the amount of carpet, we calculated the length using the perimeter, converted to feet, and found the area of the floor to be approximately 6.24 square feet. At $12.00 per square foot, the cost to carpet the doghouse is approximately $74.88.

Step-by-step explanation:

If Josh's doghouse floor has a perimeter of 122 inches and the width is 25 inches, we need to determine the length and then calculate the area. Since the perimeter of a rectangle is the sum of twice the length and twice the width (P = 2L + 2W), we can represent this relationship as:

122 inches = 2L + 2(25 inches)

122 inches = 2L + 50 inches

72 inches = 2L

L = 36 inches.

Now we convert the dimensions to feet (since 12 inches = 1 foot) and calculate the area of the floor:

L = 36 inches / 12 = 3 feet

W = 25 inches / 12 ≈ 2.08 feet

Area = Length × Width = 3 feet × 2.08 feet ≈ 6.24 square feet.

Josh needs approximately 6.24 square feet of carpet.

If carpet costs $12.00 per square foot, then:

Cost = Area × Price per square foot = 6.24 square feet × $12.00/square foot = $74.88.

Josh will have to spend approximately $74.88 to carpet the doghouse floor.

Answer 2

The Answer is: 1) 6.25 square feet. 2) Cost $75.00 of carpet.

Step-by-step explanation:

The perimeter is 122 inches. Let l be length and w be width:

2l + 2w = 122

The width is given as 25 inches:

2l + 2(25) = 122

2l + 50 = 122

2l = 72

l = 36

Area is equal to the length times the width:

a = l * w

a = 36 * 25

a = 900 square inches

Divide by 144 square inches to get square feet:

900 / 144 = 6.25 square feet.

Multiply the amount per square foot times the total cost:

$12.00 * 6.25 = $75.00

Hope this helps! Have an Awesome Day!! :-)