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

2 Answers
Feb 21, 2018

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.

Feb 21, 2018

#"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"#