A rectangular closet has an area of 108 square meters and the perimeter of 42 what is the length of the long wall of the closet?

Question

Im very slow and im in 6th grade just doing pre algebra work please help me out.

Answer 1

Hello, thank you for taking the time to post your question!

The starting point here is to take the idea that area = length x width and that the perimeter, meaning 2L + 2W, is equal to 42 to set up a system of equations:

L x W = 108

2L + 2W = 42

Substituting L = 21 - W into the first equation gives

(21 – W)*W = 108

21W – W^2 = 108

Solving that for the value of W then gives

W^2 – 21W + 108 = 0

(W – 9)(W – 12) = 0

W = 9 or W = 12

Then you can plug that back into the first equation to find the length

L = 9 or L = 12

Since it’s asking for the length of the long wall then the value here would be 12!

I hope that helps get you moving in the right direction! Feel free to reach out if you have any additional questions beyond that :)

Answer 2

Area is length x width (L x W). The closet has an area of 108 sq meters, so LW = 108 and W = 108/L

Perimeter is 2L + 2W = 42.

You can substitute the 1st equation into the 2nd equation to eliminate one of the variables;

2L + 2(108/L) = 42

Multiply both sides by L to eliminate the fraction: 2L² + 216 = 42L

Converting to quadratic form: 2L²- 42L + 216 = 0

Divide by 2: L² - 21L + 108 = 0

Factor: (L - 9)(L - 12) = 0, so L - 9 = 0 and L = 9, or L - 12 = 0 and L = 12.

Assuming the length is the longer of the two dimensions, then L = 12 and W = 108/12 = 9

Check: P = 2(12) + 2(9) = 24 + 18 = 42

Answer 3

Hi Nancy T.

Length of the longest wall is 12

Since we doing 6th grade pre-algebra can I assume that you are not familiar with Quadratics? If so please see below

For a Rectangle of length l and width w

Area = l * w

Perimeter = 2l + 2w = 2( l + w)

For your closet we can

let l = length of the longest wall of the closet

let w = width of the shortest wall of the closet

2(l + w) = 42

Divide both sides of the equation by 2

l + w = 21

Next we have the area

l * w = 108

So we need factors that multiply to 108 and add to 21

Can you factor 108 to find the numbers?