The length of a rectangular room is 7 meters less than twice its width. If the area of the room is 130m^2. How do you find the dimensions of the room?

1 Answer
Jun 4, 2018

Answer:

#13" metre"xx10" metre."#

Explanation:

If #l# and #b# are the length and breadth of the room resp., then,

by what is given, #l=2w-7#.

Hence, the area of the room is #lxxb=(2w-7)w#, which is, #130#.

#:. w(2w-7)=130 rArr 2w^2-7w-130=0#.

#:. ul(2w^2-20w)+ul(13w-130)=0#.

#:. 2w(w-10)+13(w-10)=0#.

#:. (w-10)(2w+13)=0#.

#:. w=10 or w=-13/2#, which is inadmissible.

#:. w=7" metres, "l=2w-7=13" metres"#.

So, the dimensions of the room are #13" metre"xx10" metre."#