Question

The length of a rectangle is 2 meters more than 3 times the width. If the area is 33 square meters, find the widthand the length.Width:_ metersLength:_ meters

Answer 1

Step-by-step explanation:

Let the length be

`=x`

Let the width be

`=y`

The length of a rectangle is 2 meters more than 3 times the width.

This can be represented below as

`x=3y+2`

The area of a rectangle is calculated with the formula below

`A=l* w`

By substituting the values, we will have

`\begin{gathered} A=l* w \\ A=y(3y+2) \\ 33=3y^2+2y \\ 3y^2+2y-33=0 \end{gathered}`

By factorizing the quadratic equation, we will have that

`\begin{gathered} 3y^(2)+2y-33=0 \\ 3y^2+11y-9y-33=0 \\ y(3y+11)-3(3y+11)=0 \\ y-3=0,3y+11=0 \\ y=3,3y=-11 \\ y=3,y=(-11)/(3) \end{gathered}`

Hence,

The length will be

`\begin{gathered} x=3y+2 \\ x=3(3)+2 \\ x=9+2 \\ x=11 \end{gathered}`

Hence,

The final answers are

`\begin{gathered} width=3meters \\ length=11meters \end{gathered}`