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?

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Answer 1 · 2018-06-04T19:20:28

$13" metre"xx10" metre."$

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 $13" metre"xx10" metre."$