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?

Question

Allison Allen · Accepted Answer

#P = 4s - 10 " inches"#

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#

Noah Atkinson · Answer

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

Violet Aldrich · Answer

undefined To represent the perimeter of the rectangle, you would add up the lengths of all four sides. Since the rectangle is 6 inches shorter than the square and 1 inch longer, its length would be $ s - 6 $ inches and its width would be $ s + 1 $ inches.

The perimeter ($ P $) of a rectangle is calculated by adding twice the length ($ l $) and twice the width ($ w $). Therefore, the expression to represent the perimeter of the rectangle would be:

$$ P = 2(l + w) $$

Substituting the given values for the length and width of the rectangle, we have:

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