The length of a rectangle is 3 times the width. The perimeter is 48 centimeters. What is the area?

1 Answer
Aug 11, 2017

#108cm^2#

Explanation:

So, the perimeter of any rectangle is given by adding the length twice and the width twice:

#P = L +W+L+W#

In our particular case the length is 3 times the width:

#L = 3 xx W#

Substituting that, and the 48 centimeters we know the perimeter to be into the first equation, we get:

#48=3 xx W+W+3 xx W+W#
#48=8 xx W#
#W==48/8#
#W=6#

So, if the width is 6, the length is:

#L = 3 xx W = 3 xx 6 = 18#

Now, the area of any rectangle is given by multiplying the length and the width:

#A=L xx W#

In our case #L = 18# and #W = 6#, so:

#A = 18 xx 6 = 108#

Also, remember to "multiply" the units. In this case centimeter times centimeter gives us centimete#r^2# or #cm^2#

So the area is #108cm^2#