If the perimeter is 28 meters and the area is 24 square meters what is the length and width of the rectangle?

Answer 1

First here are the formulas we will need.

Perimeter of a Rectangle:

P = 2 (W + L)

Area of a Rectangle:

A = LW

We are given that the P = 28. Plug that in:

2 (W + L) = 28

Divide by 2 on both sides to get

W + L = 14

We are given the Area is 24.

LW = 24

We can do this algebraically, but since this is listed under Elementary math, we will use this approach: Let’s see what numbers can multiply to 24:

1 x 24

2 x 12     <- add to 14

3 x 8

4 x 6

We know that W + L is 14, so which of those add to 14?

2 + 12 = 14

So our W = 2 and L = 12 Answer

Answer 2

Hello Nicole,

There are two ways to do this type of problem. The first way would be to create a system of equations to figure out the dimensions. However, for an elementary level problem, this method is too difficult. The second way would be to simply guess and check until we pick the right numbers.

We know that the perimeter of the rectangle is 28m, meaning all sides add up to 28. In a rectangle, we know that the 2 long sides have the same value (the length-L) and the 2 shorter sides have the same value (the width-W). The problem also states that the length times the width, or the area, is 24m^2.

So we know we are looking for two numbers that when multiplied together equal 24 and when added according to the perimeter equation (2L + 2W) equals 28.

First, let's list all the ways we can multiply to get a value of 24:

1 x 24

2 x 12

3 x 8

4 x 6

These are now our possible lengths and widths of the rectangle. Now, we must see which sets of numbers add to a perimeter of 28.

(2x24) = 2 + 48 = 50

(2x2) + (2x12) = 4 + 24 = 28

(2x3) + (2x8) = 6 + 16 = 22

(2x4) + (2x6) = 8 + 12 = 20

So the length of our rectangle is 12m and the width is 2m.

I hope this helps!

Answer 3

The length and width are 12 and 2, because that gives an area of 24. (Area = length x width). Also, the perimeter would be 12 + 12 + 2 + 2 = 28.