Finding the dimensions of a rectangle

The length of a rectangle is 3 times the width. If the length is decreased by 4 m and the width is increased by 1 m, the perimeter is 66 m. Find the dimensions of the original rectangle.

Let x = width
Let y = length

y = 3 * x

Perimeter is 2 * length and 2 * width:
2(y - 4) + 2(x + 1) = 66
2y - 8 + 2x + 2 = 66
2x + 2y = 72

Substitute y = 3x into the second equation and solve for x:
2x + 6x = 72
8x = 72
x = 9

Substitute x = 9 into the first equation to solve for y:
y = 9 * 3 = 27

Therefore, width = 9 m and length = 27 m

P = 2l + 2w

And in this case:

length = 3w and is decreased by 4 ------> l=3w-4

width = w and is increased by 1 --------> w=w+1

Perimeter is 66 -- so we punch everything into the formula:

66 = 2(3w-4) + 2(w+1)

66 = 6w - 8 + 2w + 2

72 = 8w

w=9 ---------> Answer for width

Now find length

l=3w
or
l = 3(9) = 27 ------> Answer for length

So the width is 9m and the length is 27m

Have a good day!

L = 3W

2(L + 4) + 2(W + 1) = 66

6W + 2W = 56 --> W = 7 m, L = 21 m