0

# What Sides of a rectangle give perimeter equal to to area?

Updated: 4/28/2022

Wiki User

13y ago

perimeter = 2 x (width + length)

area = width x length

If area = perimeter then:

width x length = 2 x width + 2 x length

width x length - 2 x length = 2 x width

length x (width - 2) = 2 x width

length = 2 x width / (width - 2)

So any rectangle with length and width that satifies the above will work, for example:

width = 2.5, length = 10, area: 2.5 x 10 = 25; perimeter: 2x(2.5+10) = 2x12.5 = 25

width = 3, length = 6, area: 3x6 = 18; perimeter: 2x(3+6) = 2x9 = 18

width = 4, length = 4, area: 4x4 = 16; perimeter: 2x(4+4) = 2x8 = 16

By making the length dependent on the width, the width must be at least 2.

Once the 4x4 square has been reached, the width becomes larger than the length, but the pair will also be given if the width is the smaller dimension, for example, a width of 6 gives a length of 2 x 6 / (6 - 2) = 12 / 4 = 3, which matches the length of 6 being given by a width of 3.

Wiki User

13y ago