Question

The length of a rectangle is two thirds its width. the area is 12 square meters. find its width. round your answer to two decimal places.

Answer 1

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