Question

( Help Please )

A farmer is searching his farmland, looking for a missing horse that went grazing in the field of newly cut hay. He finds himself on the opposite corner of where he started and wants to return to his truck as soon as possible. The field is 450 yd by 600 yd. How far will he walk if he walks diagonally across the field, and how much distance will he save instead of walking around the field? Explain your answer. Make sure to use the Pythagorean Theorem when solving this word problem.

Answer 1

750 yards

Explanation:

I entered the area of the field into a Pythagorean Theorem Calculator and it concluded that the diagonal length of the field would be approximately 750 yard.

Answer 2

300 yd saved

Explanation:

The length of the diagonal of the field is found using the Pythagorean Theorem and is

d = √( 450 yd)² + ( 600 yd)² ) = √562500 yd² = 750 yd is the diagonal distance. If, on the other hand, the farmer walks the length and width of the perimeter of the field, that would be 450 yd + 600 yd, or 1050 yd.

The farmer could spare himself 1050 - 750, or 300 yd, of walking if he crosses the field along a diagonal.