The length of a rectangle is 3 yard less than twice the width, and the area of the rectangle is 44 yd^2. How do you find the dimensions of the rectangle?

1 Answer
Alan P.
Mar 15, 2016

Length = #8# yards
Width = #11/2 = 5 1/2# yards

Explanation:

Let
#color(white)("XXX")L: " length of rectangle (in yards)"#
#color(white)("XXX")W: " width of rectangle (in yards)"#

We ar told
[1]#color(white)("XXX")L=2W-3#
and
[2]#color(white)("XXX")LW=44#

Substituting the expression #(2W-3)# from [1] for #L# in [2]
[3]#color(white)("XXX")(2W-3)W=44#

[4]#color(white)("XXX")2W^2-3W-44=0#

We could try to factor this (it can be done)
or apply the quadratic formula:
#color(white)("XXX")W=(-(-3)+-sqrt((-3)^2-4(2)(-44)))/(2(2))#

#color(white)("XXXX")=(3+-sqrt(361))/4#

#color(white)("XXXX")=(3+-19)/4#

Giving #W=22/4=11/2 rarr L=8# (using [2])

The other algebraic solution: #W=(-16)/4# is obviously extraneous since the width can not be nedgative.

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