1. The perimeter of a rectangle is 26cm. If the length is 3cm. longer than the width. What are the dimensions?

We first define our unknowns. In this problem they are looking for the dimensions. There are two dimensions, the length and the width, but since we are given that the length is 3 cm. longer than the width, if we know the width, we will be able to find the length. So

let   x =   the width.

then

x + 3 =   the length

Now the fact that the perimeter is 26cm. gives us our equation to solve. We use the formula for the perimeter,

2L + 2W = P

and substitute our formulas for the length and the width and the value of the perimeter to get

2(x + 3) + 2x = 26

Remove parentheses.

2x + 6 + 2x = 26

Combine like terms

4x + 6 = 26

Subtract 6 from both sides.

4x = 26 - 6

Notice how subtracting from both sides amounts to transposing the 6 from one side to the other.

Combine

4x = 20

Divide both sides by 4

x = 20/4

or

x = 5

Check

If the width is 5 then the length is 8.

and the perimeter is

P = 2(8) + 2(5) = 16 + 10 = 26