Question

The are of a square is 36 square feet. Which of the following measures is closest to the length of the diagonal?A).6.0ftB).6.2ftC).8.3ftD).8.5ft

Answer 1

$\begin{gathered} \text{area}=side^2 \\ 36=side^2 \\ \text{side}=\sqrt[]{36} \\ \text{side=6} \end{gathered}$

then with the Pythagorean theorem we find the diagonal

$\begin{gathered} c^2=a^2+b^2 \\ c^2=6^2+6^2 \\ c^2=36+36 \\ c^2=72 \\ c=\sqrt[]{72} \\ c=8.485 \end{gathered}$

answer: the length of the diagonal is 8.5 ft