Question

. A square picture frame occupies an area of 112 ft2 . What is the length of each side of the picture in simplified radical form? Show your work.

Answer 1

Recall that a square is just a rectangle with all sides equal.

and the area of a rectangle is just length * width.

$\bf \textit{area of a rectangle}\\\\ A=length\cdot width\quad \begin{cases} length=x\\ width=x\\ A=112 \end{cases}\implies 112=x\cdot x\implies 112=x^2 \\\\\\ \sqrt{112}=x\implies \sqrt{16\cdot 7}=x\implies \sqrt{4^2\cdot 7}=x\implies 4\sqrt{7}=x$