The width of a rectangle is 6 kilometers less than twice it's length. If its area is 56 square kilometers, how do you find the dimensions of the rectangle?

1 Answer
CW
Aug 9, 2017

#w=8# km, #l=7# km

Explanation:

Let #l, and w# be the length and the width of the rectangle, respectively.

Given that the width is #6# km less than twice the length,
#=> w=2l-6#

Area #A = w*l#
#=> 56=(2l-6)*l#
#=> 56=2l^2-6l#
#=> 2l^2-6l-56=0#
#=> l^2-3l-28=0#
#=> (l+4)(l-7)=0#
#=> l=-4,7#
As #l# can not be negative, #=> l=7#
#=> w=2l-6=(2xx7)-6=8#

Hence, #l=7# km and #w=8# km

Check :
#A=8*7=56 " km"^2# (ok)

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