Question

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?

Answer 1

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 = 110sqrt2`

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 = 2s^2 rightarrow d = ssqrt2`
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

`220/6600 \ hr = 1/30 \ hr= 2\ min`