A? rectangle's width is ?one-seventh its? length, and its perimeter is 224 m. Find the dimensions of the rectangle.

Question

A? rectangle's width is ?one-seventh

its? length, and its perimeter is 224

m. Find the dimensions of the rectangle.

Answer 1

Hi Mamum, let L represent the length of the rectangle. Then L / 7 would represent the width of the rectangle.

 

Equation for the perimeter of a rectangle:

 

P = 2L + 2W

 

Substitute for P and W:

 

P = 224 meters

 

W = L / 7

 

224 = 2L + 2 * (L/7)

 

Solve for L:

 

224 = 2L + 2L / 7

 

Multiply entire equation by 7 to clear fractions:

 

1568 = 14L + 2L

 

1568 = 16L

 

Divide both sides by 16:

 

L = 98

 

The length of the rectangle is 98 meters.

 

The width of the rectangle is 98 / 7 or 14 meters.

 

Check:

 

P = 2L + 2W

 

224 = 2 * 98 + 2 * 14

 

224 = 196 + 28

 

224 = 224

 

Values check.

 

Questions?