The length of a rectangle is one more than four times its width. if the perimeter of the rectangle is 62 meters, how do you find the dimensions of the rectangle?

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Answer 1 · 2017-01-08T23:38:55

See full process for how to solve this problem below in the Explanation:

First, let's define the length of the rectangle as #l# and the width of the rectangle as #w#.

Next, we can write the relationship between the length and width as:

#l = 4w + 1#

We also know the formula for the perimeter of a rectangle is:
#p = 2l + 2w#

Where:

#p# is the perimeter
#l# is the length
#w# is the width

We can now substitute #color(red)(4w + 1)# for #l# in this equation and 62 for #p# and solve for #w#:

#62 = 2(color(red)(4w + 1)) + 2w#

#62 = 8w + 2 + 2w#

#62 = 8w + 2w + 2#

#62 = 10w + 2#

#62 - color(red)(2) = 10w + 2 - color(red)(2)#

#60 = 10w + 0#

#60 = 10w#

#60/color(red)(10) = (10w)/color(red)(10)#

#6 = (color(red)(cancel(color(black)(10)))w)/cancel(color(red)(10))#

#6 = # or #w = 6#

We can now substitute #w# into our formula for the relationship between #l# and #w# and calculate #l#:

#l = (4 xx 6) + 1#

#l = 24 + 1#

#l =25#

The length of the rectangle is 25 meters and the width of the rectangle is 6 meters.