Question

What is the dimension of the rectangle?

Answer 1

Length = `10cm`
Width = `6cm`

Explanation:

Let the width of the rectangle be `x` cm. Therefore, the length of the rectangle is `x+4` cm.

We know that, if we decrease the width by `2cm` and the length by `5cm`, the perimeter will be `18cm`.

That means,

`2[(x-2)+(x+4-5)]=18`

`2[(x-2+x-1)]=18`

`2(2x-3)=18`

`2x-3=9`

`2x=12`

`x=6`

So, the width is `6cm` long. Then, the length will be `6+4=10cm` long.

Answer 2

`"dimensions are "10" cm by "6" cm`

Explanation:

`"let the width "=w`

`"then length "=w+4larrcolor(blue)"4 more than width"`

`"decrease length by 5 "tow+4-5tow-1`

`"decrease width by 2 "tow-2`

`• " perimeter "=(2xx"length")+(2xx"width")`

`color(white)(xxxxxxxxxx)=2(w-1)+2(w-2)`

`color(white)(xxxxxxxxxx)=2w-2+2w-4`

`color(white)(xxxxxxxxxx)=4w-6`

`"now perimeter "=18`

`rArr4w-6=18`

`"add 6 to both sides"`

`4wcancel(-6)cancel(+6)=18+6`

`rArr4w=24`

`"divide both sides by 4"`

`(cancel(4) w)/cancel(4)=24/4`

`rArrw=6`

`rArr"width "=6" cm "`

`rArr"length "=w+4=6+4=10" cm"`