The length of a rectangle is four times its width. If the area of the rectangle is 256m^2 how do you find its perimeter?

1 Answer
Apr 6, 2018

Answer:

The perimeter of the rectangle is #80# meters.

Explanation:

Here are two formulas for rectangles that we will need to solve this problem, where #l# = length and #w# = width:

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In this question, we know that:
#l = 4w#
#A = 256 m^2#

First, let's find the width:
#lw = 256#

Let's substitute the value of #4w# for #l#:
#(4w)w=256#

Multiply the #w#:
#4w^2 = 256#

Divide both sides by #4#:
#w^2 = 64#

#w = 8#

So we know that the width is #8#.

Since #l = 4w# and we have #w#, we can find the value of #l#:
#4(8)#
#32#

The width is #8# meters and the length is #32# meters.

#-------------------#

Now we find the perimeter. Remember the formula for the perimeter is #2l + 2w# as stated earlier. Since we have the values of #l# and #w#, we can solve this:
#2(32) + 2(8)#
#64 + 16#
#80#

The perimeter of the rectangle is #80# meters.

Hope this helps!