# The length of a rectangular floor is 12 meters less than twice its width. If a diagonal of the rectangle is 30 meters, how do you find the length and width of the floor?

Length = 24 m
Width = 18 m

#### Explanation:

Width (W) = W
Length (L) = $2 \cdot W - 12$
Diagonal (D) = 30

According to Pythagorean Theorem:

${30}^{2} = {W}^{2} + {\left(2. W - 12\right)}^{2}$

$900 = {W}^{2} + 4 {W}^{2} - 48 W + {12}^{2}$

$900 = 5 {W}^{2} - 48 W + 144$

$5 {W}^{2} - 48 W - 756 = 0$

$\Delta = {48}^{2} - 4 \cdot 5 \cdot \left(- 756\right) = 2304 + 15120 = 17424$

$W 1 = \frac{- \left(- 48\right) + \sqrt{17424}}{2 \cdot 5} = \frac{48 + 132}{10}$
$W 1 = 18$

$W 2 = \frac{- \left(- 48\right) - \sqrt{17424}}{2 \cdot 5} = \frac{48 - 132}{10}$
$W 2 = - 8 , 4$ (impossible)

$S o , W = 18 m$

$L = \left(2 \cdot 18\right) - 12 = 24 m$