Question

The length of a side of a rectangle is 6 cm. What should the length of the other side be so that the perimeter of the rectangle is smaller than the perimeter of a square with a side of 4 cm?

Answer 1

width < 2 cm

Explanation:

The formula for the perimeter of a rectangle is:

P = 2w + 2l, where 'w'=width and 'l'=length

The forumla for the perimeter of a square is:

P = 4s, where 's'=length of one side

The perimeter of a square with side of 4cm: P=4(4) = 16cm

Since the length of the rectangle = 6cm, we can set up an inequality to find the measure of the other side:

2w + 2(6) < 16 or 2w + 12 < 16

Subtract 12 from both sides: 2w + 12 - 12 < 16 - 12 or 2w < 4

Divide and solve: 2w/2 < 4/2 or w < 2 cm

Answer 2

The perimeter of the rectangle is smaller than the perimeter of a square with a side of 4 cm.

The length of the other side of the rectangle is 2 cm.

Given:

Length of a side of a rectangle (l) = 6 cm

Side of a square = 4cm

Let w = the width of the rectangle

Square: perimeter (p) = 4(side)

P = 4(4) = 16 cm

Rectangle: perimeter =
`2l+2w`

`2(6)+2w` <
`16`

`2w` <
`16-12`

`w` <
`(4)/(2)`

`w` <
`2` cm

Therefore, the length of the other side of the rectangle is 2 cm so that the perimeter of the rectangle is smaller than the perimeter of a square with a side of 4 cm.