Question

If the perimeter of a rectangle is 18cm and the area is 20cm then what is the length and with of the rectangle?

Answer 1

`W = 4` cm `L = 5` cm, or
`W =5` cm `L = 4` cm

Explanation:

Well let's start with equations for perimeter and area of a general rectangle:

`P= 2*L+2*W`
`A = L*W`

We know that we want `P= 18` and `A= 20` so we can plug that in:

`18 = 2*L+2*W`
`20 = L*W`

The top equation can even be simplified further by dividing everything by a 2 to equal this:

`9=L+W`

So now we have 2 equations and 2 unknowns, so we just need to solve the system of equations. First, solve for `L` in the first equation:

`L=9-W`

Plug this in to the second equation:

`20 = (9-W)*W`

Solve for `W`

`20 = 9W-W^2`
`W^2-9W+20=0`
`(W-5)(W-4)=0`
`W=4,5`

Plug these solutions back into `9=L+W`

When `W=4` `L=9-4=5`
When `W=5` `L=9-5=4`

So the box has a width and length of 5 cm and 4 cm, it doesn't matter which one is which as long as the other is the opposite.

Hope this helped!