# Triangle A has an area of 4  and two sides of lengths 5  and 3 . Triangle B is similar to triangle A and has a side with a length of 32 . What are the maximum and minimum possible areas of triangle B?

$113. \dot{7}$ or $163.84$
if the 32 corresponds to the side of 3 then it is a multiplier of $10 \frac{2}{3}$, ( $\frac{32}{3}$). The area would be $4 \times {\left(\frac{32}{3}\right)}^{2} = \frac{1024}{9} = 113. \dot{7}$
$\left(\frac{32}{5}\right)$ The area would be $4 \times {6.4}^{2} = \frac{4096}{25} = 163.84$