Question

If you cut away a triangle of area 59 cm² from a square, the remaining area will be 85 cm². Find the length of the side of the square before it was cut.

Answer 1

So the square was fine, then the triangle decided to go for a hike.

now, if the triangle when it took off, it took 59 cm², and the square was left all by its lonesome with only 85 cm², that means with the triangle in it, the square is then 59 + 85 cm², or 144 cm².

$\bf \textit{area of a square}\\\\ A=s^2\qquad \begin{cases} s=\textit{length of a side}\\ ---------\\ A=144 \end{cases}\implies 144=s^2 \\\\\\ \sqrt{144}=s \implies 12=s$