The plans for a shed call for a rectangular floor with a perimeter of 198 ft. The length is The two times the width. How do you find the length and width?

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Answer 1 · 2017-01-07T21:21:03

See full explanation for how to find the length and width below in the explanation:

The formula for a perimeter is:

#p = 2w + 2l#

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

And, we know from the problem:

#l = 2w#

We can then substitute #2w# for #l# in the equation for the perimeter to give:

#p = 2w + (2 xx 2w)#

#p = 2w + 4w#

#p = 6w#

We also know the perimeter will be 198 ft so we can substitute this for #p# and solve for #w#, the width:

#198 = 6w#

#198/color(red)(6) = (6w)/color(red)(6)#

#33 = w# or #w = 33#

And because we know:

#l = 2w# we can substitute #33# for #w# and solve for #l#:

#l = 2 xx 33#

#l = 66#

The length of the floor will be 66 ft and the width will be 33 ft.