The area of a square field is 24,200 m^2. How long will Maya take to cross the field diagonally at the rate of 6.6 km/hr?

Mar 4, 2018

2 minutes

Explanation:

If a square field has area 24200 ${m}^{2}$, then we can find out its side length, s, in meters:

${s}^{2} = 24200 = 2 \cdot 121 \cdot 100 = 2 \cdot {11}^{2} \cdot {10}^{2}$
$s = 110 \sqrt{2}$

We can use Pythagorean theorem to find out the length of the diagonal, d, in meters:
${s}^{2} + {s}^{2} = {d}^{2} \rightarrow {d}^{2} = 2 {s}^{2} \rightarrow d = s \sqrt{2}$
so $d = 220$.

If Maya's speed is 6.6 km/hr that means it's 6600 m / hr. She has to run 220 meters, so she will take

$\frac{220}{6600} \setminus h r = \frac{1}{30} \setminus h r = 2 \setminus \min$