SOLUTION: A field is 175 yd long from end to end and 180 ft. Wide. If a person runs diagonally across the field from one end to the other, how far does he run?

Algebra ->  Pythagorean-theorem -> SOLUTION: A field is 175 yd long from end to end and 180 ft. Wide. If a person runs diagonally across the field from one end to the other, how far does he run?      Log On


   

Question 1091894: A field is 175 yd long from end to end and 180 ft. Wide. If a person runs diagonally across the field from one end to the other, how far does he run?
Found 2 solutions by josgarithmetic, greenestamps:
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
As yards,
sqrt%28175%5E2%2B%281%2F3%29%281%2F3%29180%5E2%29

sqrt%2830625%2B60%2A60%29

sqrt%2834225%29

185, yards.

Answer by greenestamps(13200) About Me  (Show Source):
You can put this solution on YOUR website!

First of all, you need to notice the different units used for the length and width; you need to convert one of them so that your units are consistent.

180 feet is 60 yards; so the dimensions of the field are 175x60 yards.
Since this is a rectangular field, the diagonal will form a right triangle with the sides. So you are looking for the hypotenuse of a right triangle with legs 175 and 60.

You could of course just plug those numbers into a calculator to find the length of the diagonal. However, if you are good with numbers you can find the answer relatively easily.

The dimensions 175 and 60 are both multiples of 5, so we can think of a "scale model" of the field with dimensions 35 and 12.

Then you might recognize those numbers as the two legs of a Pythagorean triple of numbers, 12-35-37. So the diagonal in your scale model has length 37; that means the diagonal of the actual field has length 37*5 = 185.