A square has sides of length #s#. A rectangle is #6# inches shorter than the square and #1# inch longer. How do you write an expression to represent the perimeter of the rectangle?

2 Answers
Lotusbluete
Dec 4, 2015

#P = 4s - 10 " inches"#

Explanation:

Let's say that the rectangle has sides #a# and #b#.

You already know that #a = s - 6# and #b = s + 1#.

The perimeter of a rectangle is

#P = 2 * (a + b) = 2 (s - 6 + s + 1) = 4s - 10#

Ms. Worth
Dec 18, 2017

The Perimeter of the rectangle in inches can be represented as
#4s - 10#

Explanation:

Problems like this can be confusing because it's hard to know how to write the math for all those measurements.

The trick is to do it one step at a time.

Let #s# represent the length of a side of the square

Length of the side . . . . .#s# #larr# length of the side of the square
6 inches shorter . . . . . . #s - 6# #larr# length of rectangle
1 inch longer . . . . . . . . . #s + 1# #larr# width of rectangle

Perimeter is found by adding both widths plus both lengths

#P = [b##oth  widths]  plus  [b##oth# #l#e#ng##ths#]
#P = [color(white)(..)2color(white)(.)(s + 1)] color(white)(.)+ color(white)(.)[color(white)(.)2color(white)(..)( s - 6)color(white)(.) ]#

#P = 2(s + 1) + 2( s - 6)#

1) Clear the parentheses by distributing the twos
#P = 2s + 2 + 2s - 12#

2) Combine like terms
#P = 4s - 10# #larr# answer

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