Find the length and width.

Question

Find the length and width.
The plans for a shed call for a rectangular floor with a perimeter of 296 ft. The length is three times the width. Find the length and width.

The width is ___ ft. The length is ___ ft.

Answer 1

Hi Kenny,

 

You have two unknowns, (length and width), so you'll need two equations.  

 

The formula for the perimeter of a rectangle is, length + length + width + width = perimeter.  A rectangle has opposite sides parallel and congruent, so I can just say that the lengths are the same and the widths are the same.

 

So,

 

2L + 2W = 296  (two times the length and two times the width is 296)

 

Next,  Your problem says that the length is 3 times the width.  Written as an equation that would look like

 

L = 3W

 

Now, I'll just substitute 3W for L back into the first equation.

 

2 (3W) + 2W = 296     (substitution)

6W + 2W = 296          (multiply the 2 and 3W)

8W = 296                   (combine like terms)

W = 37                       (divide by 8)

 

Now, lets plug that 37 back into the second equations to find L.

 

L = 3W

L = 3 (37)

L = 111

 

So the width of the rectangle is 37 and the length is 111.

 

You can verify that the numbers work by plugging both back into the first equation.

 

2(111) + 2(37) = 296.   Yep, that checks.

 

Hope that helps!

 

Answer 2

let L and W be the length and width of the floor:

• perimeter of 296 ft: Perimeter = 296 ft = 2L + 2W
• The length is three times the width: L = 3W

 

Substitute 3W in place of L in the perimeter equation:

 

296 = 2L + 2W

296 = 2(3W) + 2W

296 = 6W + 2W

296 = 8W

 

Solve for W.  Once you have W, L = 3W.