Question

Find the approximate length of diagonal across a square field which has an area of $22,500$ square feet.

• A. $150$ feet
• B. $178$ feet
• C. $191$ feet
• D. $212$ feet
• E. $260$ feet

Answer 1

The correct option is D $212$ feet

Area of the square$=$(side)${}^2$

$\therefore 22500=$(side)${}^2$

$\Rightarrow$ side $=\sqrt{22500}$

$\Rightarrow$ side $=150$ feet

In the above diagram Diagonal $AC=\sqrt{(AB{)}^2+(BC{)}^2}$

$\Rightarrow AC=\sqrt{22500+22500}$

$\Rightarrow AC=\sqrt{45000}$

$\Rightarrow AC=212.13\simeq 212$ feet