# 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?

Jun 4, 2018

$13 \text{ metre"xx10" metre.}$

#### Explanation:

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

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

Hence, the area of the room is $l \times b = \left(2 w - 7\right) w$, which is, $130$.

$\therefore w \left(2 w - 7\right) = 130 \Rightarrow 2 {w}^{2} - 7 w - 130 = 0$.

$\therefore \underline{2 {w}^{2} - 20 w} + \underline{13 w - 130} = 0$.

$\therefore 2 w \left(w - 10\right) + 13 \left(w - 10\right) = 0$.

$\therefore \left(w - 10\right) \left(2 w + 13\right) = 0$.

$\therefore w = 10 \mathmr{and} w = - \frac{13}{2}$, which is inadmissible.

$\therefore w = 7 \text{ metres, "l=2w-7=13" metres}$.

So, the dimensions of the room are $13 \text{ metre"xx10" metre.}$