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

1 Answer
Feb 23, 2018

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=2L+2W
A=LW

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

18=2L+2W
20=LW

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=9W

Plug this in to the second equation:

20=(9W)W

Solve for W

20=9WW2
W29W+20=0
(W5)(W4)=0
W=4,5

Plug these solutions back into 9=L+W

When W=4 L=94=5
When W=5 L=95=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!