# The area of a rectangular floor is described by the equation w(w-9)=252 where w is the width of the floor in meters. What is the width o the floor?

Jun 3, 2016

Width $\left(w\right) = 21$

#### Explanation:

Given:
$w \left(w - 9\right) = 252$

Multiply everything inside the brackets by $w$

$\implies {w}^{2} - 9 w = 252$

Subtract 252 from both sides

${w}^{2} - 9 w - 252 = 0$

Factors of 252 that have a difference of 9 are 12 and 21
We need -9 so the larger if the two is negative.

$\left(w - 21\right) \left(w + 12\right) = {w}^{2} + 12 w - 21 w - 252 \textcolor{red}{\text{ Works}}$

So
$w - 21 = 0 \text{ " =>" } w = + 21$
w+12=0" "=>" "w=-12 color(red)(larr" negative value not logical")

Width $\left(w\right) = 21$