Question

The perimeter of a rectangular atrium is 160 feet. The length is 16 feet more than the width. Find the length and width of the atrium.

Short answer

The length of the atrium is 48 feet and the width is 32 feet.

Step-by-step solution

Step 1. Given Information

• The perimeter of the atrium is 160 feet.
• The length of the atrium is 16 feet more than the width.

Step 2. Define the Variables

• Assume that the width of the atrium is w.
• So, the length of the atrium is $w+16$.

Step 3. Use the Perimeter Formula

• Substitute $P=160$feet and $l=w+16$in the formula of perimeter of a rectangle and solve to find the missing variable.

$$\begin{gathered} 160=2\left(w\right)+2\left(w+16\right) \\ 160=4w+32 \\ 4w=128 \\ w=32 \end{gathered}$$

• So, the width of the rectangle is 32 feet.

Step 4. Find the Length

• Substitute $w=32$in $l=w+16$and solve to find the length of the atrium.

$$\begin{gathered} l=32+16 \\ =48 \end{gathered}$$

• So, the length of the atrium is 48 feet.

Step 5. Conclusion

The length of the atrium is 48 feet and the width is 32 feet.