The width of a rectangle is 9 cm less than twice the length. The perimeter is 72 cm. What is the length and width of the rectanlge?Equation: Solution:

The problem as stated is a two variable problem.  That
means there are two quantities in the problem which are unknown: the length and the
width.  To solve problems of this nature there must be two equations which relate the
two unknown variables.  In this case, we use the formulae for the perimeter and the
given relationship between the length and the width.

`P =
2L + 2W`

and

`W =
2L-9`

Substitute the expression for the width into the
equation for the perimeter:

`P = 2L +
2(2L-9)`

Expand the parenthesis by applying the
distributive property and replace P with the given value for the
perimeter:

`72 = 2L + 4L -
18`

Collect similar terms on the right side of the
equation, add 18 to both sides, and apply the symmetric property of
equality:

`72 = 6L -
18`

`6L =
90`

Divide both sides by 6 to determine that the length is
15.

Substitute this back into the width equation to
determine W:

`W = 2x15 - 9 =
21`

Check your answer by computer the
perimeter:

2x15 + 2x21 = 30 +42 =
72

State the answer using proper units of
measure:

L = 15 cm and W = 21 cm or "The
length of the rectangle is 15 cm and the width is 21
cm"