# The length and width of a rectangle are 3x+1, and x+1, respectively. If the perimeter of the rectangle is 28, how long is each side?

##### 2 Answers

#### Explanation:

sum of parts = perimeter = 28

2 sides + 2 lengths = 28

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Subtract 3 from both sides

Divide both sides by 8

length = 10 units , width = 4 units.

#### Explanation:

The opposite sides of a rectangle are

#color(blue)"equal in length"#

#rArr"perimeter" = 2(3x+1)+2(x+1)# Also the perimeter = 28.

Thus, equating the 2 values for the perimeter gives.

#2(3x+1)+2(x+1)=28larr" equation to be solved "# distribute the brackets.

#6x+2+2x+2=28# collect like terms on left side.

#rArr8x+4=28# subtract 4 from both sides.

#8xcancel(+4)cancel(-4)=28-4#

#rArr8x=24# To solve for x, divide both sides by 8.

#(cancel(8) x)/cancel(8)=24/8#

#rArrx=3" is the solution to the equation"# Length of rectangle

#=3x+1=(3xx3)+1=10" units"# Width of rectangle

#=x+1=3+1=4" units"# check :

#(2xx10)+(2xx4)=20+8=28 color(white)(xx)✔︎#