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Chapter 2: Q. 222 (page 146)

The length of a rectangle is five inches more than twice the width. The perimeter is 34 inches. Find the length and width.

Short Answer

Expert verified

The length of the rectangle is 13 inches and the width is 4 inches.

Step by step solution

01

Step 1. Given Information 

  • The perimeter of a rectangle is 34 inches.
  • The length of the rectangle is 5 inches more than two times the width.
02

Step 2. Define the Variables

  • Let the width of the rectangle is w inches.
  • So, the length of the rectangle will be2w+5 inches.
03

Step 3. Use the Perimeter Formula

  • Substitute P=34and l=2w+5into the formula of the perimeter of a rectangle, P=2l+2wand solve to find the unknown variable.
  • 34=22w+5+2w34=6w+106w=24w=4
  • So, the width of the rectangle is 24 inches.
04

Step 4. Find the Length

  • Substitute w=4into l=2w+5and solve to find the length.

l=2×4+5=8+5=13

  • So, the length is 13 inches.
05

Step 5. Conclusion

The length of the rectangle is 13 inches and the width is 4 inches.

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