Answer:
The dimensions of the carpet are 15 inches and 82 inches
Step-by-step explanation:
Assume that the width of the carpet is x inches
∵ The width of the carpet is x inches
∵ The length of the carpet is 67 inches more than the width
∴ The length of the carpet is (x + 67) inches
∵ The perimeter of the rectangle = 2(length + width)
∵ The perimeter of the carpet = 194 inches
→ Equate the two right sides of the perimeter
∴ 2(length + width) = 194
→ Divide both sides by 2
∴ length + width = 97
→ Substitute the value of the length and width in the equation above
∵ x + 67 + x = 97
→ Add the like terms in the left side
∴ (x + x) + 67 = 97
∴ 2x + 67 = 97
→ Subtract 67 from both sides
∵ 2x + 67 - 67 = 97 - 67
∴ 2x = 30
→ Divide both sides by 2
∴ x = 15
∵ x represents the width of the carpet
∴ The width of the carpet is 15 inches
∵ The length of the carpet = 15 + 67
∴ The length of the carpet is 82 inches
∴ The dimensions of the carpet are 15 inches and 82 inches
