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!