Question

Paulina is remodeling her bathroom. the tile she has chosen are squares and trapezoids. the side length of each square inthe tile is x centimeters. the height and the length of one of the bases of each trapezoid is x centimeters. the other length is 2x centimeters. Write a simplified equation to solve for x in terms of At, the area of the tile. if necessary, use rational coefficients instead of root symbols

Answer 1

Check the picture below.

is not very specific above, but sounds like it's asking for an equation for the trapezoid only, mind you, there are square tiles too.

but let's do the trapezoid area then, 

$\bf a^{\frac{{ n}}{{ m}}} \implies \sqrt[{ m}]{a^{ n}} \qquad \qquad \sqrt[{ m}]{a^{ n}}\implies a^{\frac{{ n}}{{ m}}}\\\\ -------------------------------$

$\bf A=\cfrac{h(a+b)}{2}\quad \begin{cases} A=At\\ a=x\\ h=x\\ b=2x \end{cases}\implies At=\cfrac{x(x+2x)}{2} \\\\\\ At=\cfrac{x(3x)}{2}\implies At=\cfrac{3x^2}{2}\impliedby \textit{now, solving for \underline{x}} \\\\\\ 2At=3x^2\implies \cfrac{2At}{3}=x^2\implies \sqrt{\cfrac{2At}{3}}=x\implies \left( \frac{2At}{3} \right)^{\frac{1}{2}}=x$