## Algebra 1

$x= -15 + 15\sqrt 5$
The given ratio of $\frac{l}{w}$ is $\frac{1 + \sqrt 5}{2}$ $\frac{30}{w}$ = $\frac{1 + \sqrt 5}{2}$ We cross multiply the fractions (30)(2) = (1 + \sqrt 5)(w) We divide both sides by $(1 + \sqrt 5)$ $w = \frac{60}{(1 + \sqrt 5)}$ We multiply the fraction by the conjugate which is $(1 - \sqrt 5)$ $w = \frac{60}{(1 + \sqrt 5)} \times \frac{(1 - \sqrt 5)}{(1 - \sqrt 5)}$ Use FOIL to simplify. FOIL: First (Multiply the first variables in the brackets), outside (Multiply the outer variables), Inside (Multiply the inside variables), Last (Multiply the last variables in the brackets). $w = \frac{60 - 60 \sqrt 5}{(1 - \sqrt 25)}$ The square root of 25 is 5 because 5 x 5 is 25 $w = \frac{60 - 60 \sqrt 5}{(1 - 5)}$ $w = \frac{60 - 60 \sqrt 5}{(-4)}$ We divide the numerator coefficients by -4 $w = \frac{60}{-4} - \frac{60}{-4} \sqrt 5$ We simplify the division $x= -15 + 15\sqrt 5$