The length of a rectangle is 4 meters longer than 3 times the width. The perimeter of the rectangle is 72 meters. What is the width of the rectangle?

Answer 1

P = 2L + 2W -- perimeter formula

72 = 2(3W + 4) + 2W -- substituting variables for what we know in problem

72 = (6W + 8) + 2W -- multiply first section parentheses

72 = 8W + 8 -- simplifying by combining like terns

64 = 8W -- subtract 8 from both sides to isolate our width variable

8 = W -- solving for W...finally

So the width of the rectangle is 8 meters. Don't forget to put meters or it'll be marked wrong.

Answer 2

The formula for the perimeter of a rectangle is 2L + 2W = P, where L = Length (representing the 2 larger sides which is why L is multiplied by 2 in the formula), W = Width (representing the shorter sides which is why W is multiplied by 2 in the formula) and P = Perimeter.

We need to get the problem into a form where we are dealing with only one variable. The problem said that the "length" of the rectangle is 4 meters longer than 3 times the width so lets express length in terms of W:

L= 3W+4

Plug this back into the formula of 2L + 2W = P. Also let's replace P with 72 as we are told that in the problem

2(3W+4) + 2W = 72

Using the distributive property, let's figure 2(3W+4) like this

2(3W) + 8 + 2W = 72

The bolded portion is 6W so now the equation looks like this

6W + 8 + 2W = 72

Now combine like terms:

8W+8 = 72

Solve for W by subtracting 8 from both sides of the equation which cancels out the 8 on the left side of the equals sign and 72 - 8 is 64 so now the equation is:

8W = 64

Divide both sides by 8 which cancels out the 8 on the left side and 64/8 is 8 so the width of the rectangle is 8 meters