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 will be 66 m. Find the dimensions of the original rectangle

Length = 27 metres

Width = 9 metres

Step-by-step explanation:

Consider the width to be x.

Then the length will be 3x.

The perimeter is 66m when the width is increased by 1m and the length is decreased by 4m.

So the dimensions will become:

Length=3x-4

Width=x+1

Now solve for the variable x using the formula for perimeter of a rectangle:

P = 2 (l+b)

66 = 2 (3x-4+x+1) (Divide both sides by 2 and simplify the parentheses)

33 = 4x-3 (Add 3 to both sides)

36 = 4x (Divide both sides by 4)

x = 9

Now plug-in the value of x into the original dimensions which were:

Length=3x

Width=x

So the dimensions are:

Length = 27 metres

Width = 9 metres