the perimeter of a rectangle is 56 m. the width of the rectangle is 4 m less than the length. find the length and width of the rectangle
W = L - 4
P = 2 W + 2 L
P = 2 ( W + L )
P = 2 ( L - 4 + L )
P = 2 ( 2 L - 4 )
P = 2 * 2 L - 2 * 4
P = 4 L - 8
56 = 4 L - 8 Add 8 to both sides
56 + 8 = 4 L - 8 + 8
64 = 4 L Divide both sides by 4
64 / 4 = 4 L / 4
16 = L
L = 16 m
W = L - 4 = 16 - 4 = 12 m
Proof:
P = 2 ( W + L ) = 2 * ( 12 + 16 ) = 2 * 28 = 56 m
To find the length and width of the rectangle, we can set up and solve a system of equations based on the given information.
Let's denote:
- Length of the rectangle as 'L'
- Width of the rectangle as 'W'
We are given two pieces of information:
1. The perimeter of the rectangle is 56 m: Perimeter = 2(L + W) = 56
2. The width is 4 m less than the length: W = L - 4
First, let's work with the second piece of information:
W = L - 4
Next, we'll substitute this expression for 'W' into the perimeter formula:
2(L + (L - 4)) = 56
Simplifying the equation:
2(2L - 4) = 56
4L - 8 = 56
4L = 56 + 8
4L = 64
L = 64 / 4
L = 16
Now that we have found the length (L = 16), we can substitute this value back into our second equation to find the width:
W = L - 4
W = 16 - 4
W = 12
Therefore, the length of the rectangle is 16 m and the width is 12 m.