Question

A rectangular rug has perimeter 240 inches. The length is 12 inches more than twice the width. Find the length and width of the rug.

Short answer

The length of the rug is 84 inches and the width is 36 inches.

Step-by-step solution

Step 1. Given Information 

• The perimeter of the rug is 240 inches.
• The length of the rectangular rug is 12 more than twice its width.

Step 2. Define the Variables

• Let the width of the rectangle is w.
• So, the length of the rug is$2w+12$.

Step 3. Use the Perimeter Formula

• Use the formula of the perimeter of the rectangle, $P=2w+2l$and substitute $l=2w+12$.
• Solve the equation to find the value of unknown variable.

$$\begin{gathered} 240=2\left(w\right)+2\left(2w+12\right) \\ 240=6w+24 \\ 6w=216 \\ w=36 \end{gathered}$$

• So, the width of the rug is 36 inches.

Step 4. Find the Length

• Substitute $w=36$into $l=2w+12$and solve for the length of the rug.

$$\begin{gathered} l=2\left(36\right)+12 \\ =72+12 \\ =84 \end{gathered}$$

• So, the length of the rug is 84 inches.

Step 5. Conclusion

The length of the rug is 84 inches and the width is 36 inches.