The length of a rectangle is 5 times it’s width. The perimeter of the rectangle is at most 104 meters. Find the greatest possible dimensions of this rectangle.

Question

Write an inequality and solve the problem algebraically. 

Answer 1

Hi Vanessa, let l represent the length and w the width. Given l = 5w and the perimeter is at most 104 meters. Set up an inequality based on the equation for the perimeter of a rectangle, p = 2w + 2l.

 

 

2w + 2l ≤ 104

 

Substitue for l:

 

2w + 2 * 5w ≤ 104

 

Combine terms:

 

12w ≤ 104

 

w ≤ 8 and 2/3

 

The width is less than or equal to 8 and 2/3 meters.

 

l = 5w, or l ≤ 43 and 1/3

 

The length is less than or equal to 43 and 1/3 meters.

 

Check:

 

2 * 43 1/3 + 2 * 8 2/3 ≤ 104

 

86 2/3 + 17 1/3 ≤ 104

 

104 ≤ 104

 

Questions?