Question

A rectangular room is 5 meters longer than it is wide,and it's perimeter is 26 meters. What isthe dimension of the room?

Answer 1

The room is 4 feet wide and 9 feet long.

Explanation:

The best way to solve word problems like this is to create an equation.

The room is five meters longer than its width. If the width is represented by `x`, then the length has to be `x + 5`.

Now, how many sides does a rectangle have? 4. 2 of these sides are the width of the rectangle and the other 2 sides are the length of the rectangle, whose combined total length, the perimeter, is equal to 26 meters.

`x + x + (x+5) + (x+5)=26`

`4x+10=26`

`4x=16`

`x=4`

We are told that the room is longer than it is side, so the width is 4 meters, and the length is `x+5` meters long. The length is 9 meters.

Answer 2

`"length "=9" m and width "=4" m"`

Explanation:

`"let the width of the room "=w`

`"then the length "=w+5larrcolor(blue)"5 m lomger than width"`

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

`rArr"perimeter "=2w+2(w+5)`

`color(white)(rArr"perimeter ")=2w+2w+10=4w+10`

`"now perimeter "=26`

`rArr4w+10=26`

`"subtract 10 from both sides"`

`4wcancel(+10)cancel(-10)=26-10`

`rArr4w=16`

`"divide both sides by 4"`

`(cancel(4) w)/cancel(4)=16/4`

`rArrw=4`

`"width "=w=4" m"`

`"length "=w+5=4+5=9" m"`