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.

Related questions
See all questions in Linear, Exponential, and Quadratic Models
Impact of this question
7981 views around the world
You can reuse this answer
Creative Commons License