Question

The perimeter of a rectangle is `36`m. The area is `65m^2`. Find the length of the rectangle?

Answer 1

`13cm`

Explanation:

`P = 2(l+w)`

perimeter = 2 * (length + width)

`A = lw`

area = length * width

here, `P = 36` and `A = 65`

`2(l+w) = 36`, `lw = 65`

`2(l+w) = 36 rarr l+w = 18`

`l = 65/w`

`l = 18 - w`

`65/w = 18 - w`

`18w - w^2 = 65`

`18w - w^2 - 65 = 0`

`-w^2 + 18w - 65 = 0`

`w^2-18w+65 = 0`

this can be factorised to give `(w-13)(w-5) = 0`

`w-13 = 0 or w-5 = 0`

`w = 13 or w=5`

if the length is the longer side, then the width is the shorter side.

this means that the width must be smaller than `9cm`, and so it is `5cm`.

`w = 5`

`l = 18 - w`

`= 18-5 = 13`

the length is `13cm`.