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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