Question

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?

Answer 1

`x=25/8" "->" "x= 3 1/8`

Explanation:

`color(blue)("Building the model")`

sum of parts = perimeter = 28

2 sides + 2 lengths = 28

`2(x+1)+2(3x+1)=28`

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`color(blue)("Solving for "x)`

`2x+2+6x+1=28`

`8x+3=28`

Subtract 3 from both sides

`8x=25`

Divide both sides by 8

`x=25/8`

Answer 2

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)✔︎`