Question

A given rectangle has an area of `x^2-3x` and a width of `x`. What is the rectangle's length?

Answer 1

The rectangle's length is `x-3`.

Explanation:

We know that the area of a rectangle can be defined as:

`color(white)=>A_"rectangle"="length"xx"width"`

which can be rearranged to be:

`color(white)=>A_"rectangle"/"width"="length"`

Now, we can plug in our values; we know that the area is `x^2-3x` and the width is `x`:

`color(white)=>A_"rectangle"/"width"="length"`

`=>(x^2-3x)/x="length"`

`color(white)=>(x^color(red)cancelcolor(black)2-3color(red)cancelcolor(black)x)/color(red)cancelcolor(black)x="length"`

`color(white)=>(x-3)/1="length"`

`color(white)=>x-3="length"`

That's the answer. Hope this helped!

Answer 2

`L=x-3`

Explanation:

Area of a rectangle`=LxxW`

`:.LxxW=x^2-3x` and `W=x`

`:.xxxL=x^2-3x`

`:.L=(x^2-3x)/x`

`:.L=(cancelx^1(x-3))/cancelx^1`

`:.L=x-3`