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A rectangular carpet has a perimeter of 194 inches. The length of the carpet is 67 inches more than the width. What are the dimensions of the​ carpet?

User Txema
by
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1 Answer

6 votes

Answer:

The dimensions of the carpet are 15 inches and 82 inches

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

User Sergej Isbrecht
by
7.9k points
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