Question

The perimeter of a rectangle is 34 cm. The length is 1 cm longer than the width. What is the length of the longest side of the rectangle?

Answer 1

Answer: 9 cm

Explanation:

The formula for the perimeter of a rectangle is
`2l+2w=P`

Where

l is the length

w is the width

and P is the perimeter (34)

Because the length is 1 cm longer than the width instead of representing the length is l we can use w+1

Sub in the known values and solve

Step 1: Simplify both sides of the equation with the Distributive Property

`2(w+1)+2w=34\\(2)(w)+(2)(1)+2w=34\\2w+2+2w=34\\(2w+2w)+(2)=34\\4w+2=34\\`

Step 2: Subtract 2 from both sides.

`4w+2-2=34-2\\4w=32`

Step 3: Divide both sides by 4.

`(4w)/(4)=(32)/(4) \\w=8`

Step 4: Add 1 to w to find the length of the longer side

`w+1\\8+1\\9`