Question

If the area of a square is 38 less than 2 times the area of a hexagon, and the sum of the areas of the square and hexagon is 46, what are the areas of the square and hexagon?

Answer 1

$\bf \begin{cases} s=\textit{area of the square}\\ h=\textit{area of the hexagon} \end{cases} \\\\\\ \textit{38 less than 2 times the area of a hexagon}\implies \boxed{s}=2h-38 \\\\\\ \textit{we also know that their sum is }\implies s+h=46 \\\\\\ \boxed{2h-38}+h=46\implies 3h=46+38\implies 3h=84 \\\\\\ h=\cfrac{84}{3}\implies h=28$

what's the area of the square?  well, s = 2h - 38.

Answer 2

Hexagon is 8 and the square is 24