Question

a square field has an area of 22,500 square feet. to the nearest foot, what is the diagonal distance across the field?
150 feet
178 feet
191 feet
212 feet

Explanation:

Step1: Find side - length of the square

Let the side - length of the square be $s$. The area of a square is $A = s^{2}$. Given $A = 22500$ square feet, then $s=\sqrt{22500}=150$ feet.

Step2: Use the Pythagorean theorem to find the diagonal

In a square, if the side - length is $s$ and the diagonal is $d$, by the Pythagorean theorem $d^{2}=s^{2}+s^{2}$. Since $s = 150$ feet, $d^{2}=150^{2}+150^{2}=2\times150^{2}$. Then $d = 150\sqrt{2}\approx150\times1.414 = 212.1$ feet.

Answer:

212 feet