Question

the length of a rectangle is 3 times its width. if the length were increased by 2 with perimeter of 72 what's the new perimeter

Answer 1

`Perimeter_(newrec\tan gle)=76`

Step-by-step explanation

To find the perimeter of a rectangle, add the lengths of the rectangle's four sides.

`\begin{gathered} \text{Perimeter}=\text{ 2}\cdot length+2\cdot width \\ Perimeter_(rec\tan gle)=2(\text{length}+\text{widht)} \end{gathered}`

Step 1

Let

W represents the width

L represents the lengh

hence,the length of a rectangle is 3 times its width.

traslate,

`L=3W\rightarrow equation(1)`

and the perimeter is 72,so

`\begin{gathered} Perimeter_(rec\tan gle)=2(\text{length}+\text{widht)} \\ 72=2(L+W)\rightarrow equation(2) \end{gathered}`

Step 2

solve the equations:

a)replace equation (1) in equation (2)

`\begin{gathered} 72=2(L+W)\rightarrow equation(2) \\ 72=2(3W+W) \\ 72=6W+2W \\ 72=8W \\ \text{divide both sides by 8} \\ (72)/(8)=(8W)/(8) \\ 9=W \end{gathered}`

it means the width is 9 units

b)

now, replace the W value in equation (1)

`\begin{gathered} L=3W\rightarrow equation(1) \\ L=9\cdot3 \\ L=27\text{ units} \end{gathered}`

so, for the original rectangle

`\begin{gathered} \text{length= 27 units} \\ \text{width}=9\text{ units} \end{gathered}`

Step 3

now , find the new perimeter if the length were increased by 2

Let

Length= 27 units + 2 units=29 units

width=9 units

replace to find the perimeter

`\begin{gathered} Perimeter_(rec\tan gle)=2(\text{length}+\text{widht)} \\ Perimeter_(rec\tan gle)=2(\text{29+9)} \\ Perimeter_(rec\tan gle)=2(\text{38)} \\ Perimeter_(newrec\tan gle)=76 \end{gathered}`

I hope this helps you