L = [tex]( \frac{2}{3} )[/tex]w
a = 12
Length times width = area
L · w = a
[tex]( \frac{2}{3} )[/tex]w · w = 12
[tex]( \frac{2}{3} )[/tex] [tex] w^{2} [/tex] = 12
Divide both sides by [tex] \frac{2}{3} [/tex] or mulitply both sides by [tex] \frac{3}{2} [/tex] (either one is fine)
[tex]( \frac{2}{3} )[/tex] ÷ [tex]( \frac{2}{3} )[/tex] [tex] w^{2} [/tex] = 12 ÷ [tex]( \frac{2}{3} )[/tex]
or
[tex]( \frac{3}{2} )[/tex] [tex]( \frac{2}{3} )[/tex] [tex] w^{2} [/tex] = 12 [tex]( \frac{3}{2} )[/tex]
[tex] w^{2} [/tex] = 18
Square root both sides to get rid of the squared on the w
[tex] \sqrt{w^{2} } [/tex] = [tex] \sqrt{18} [/tex]
w = 4.24
