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= 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!