area and length

Question

The area of a rectangle is
44 m2
, and the length of the rectangle is
3 m
less than double the width. Find the dimensions of the rectangle.

Answer 1

The area of a rectangle is found by the product of

length and width:  A = LW

 

1)  LW = 44

 

Length is 3m less than double the width:

2)  L = 2W - 3

 

Substitute 2W-3 in place of L in the first equation

to solve for width

 

(2W-3)W = 44   multiply the W through the parenthesis

2W² - 3W = 44   Subtract 44 from both sides

2W² - 3W - 44 = 0

 

We have a quadratic.  We can try to factor.  Failing that

we can use the quadratic equation to solve for W

 

Multiply the coefficient of the square term (2) by the

constant (-44)... 2(-44) = -88.   Look for factors of

-88 that add to the coefficient of the W term (-3):

(-11)(8) = -88.  -11+8=-3.  Replace the

-3W with -11W + 8W and factor by grouping

 

2W²-3W-44 = 0

2W²+8W-11W-44=0

2W(W+4) -11(W+4)=0

(2W-11)(W+4) = 0

 

Either 2W-11 = 0

         2W = 11 

         W = 11/2 or 5.5m

 

OR  W+4=0

      W=-4m

 

Since the width will not be a negative, discard W = -4

The width of the rectangle is 5.5m

 

L = 2W-3 = 2(5.5)-3 = 11-3 = 8m

The length of the rectangle is 8m

 

The rectangle is 8m by 5.5m