document.write( "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? \n" ); document.write( "

Algebra.Com's Answer #706389 by greenestamps(13200) $\"\"$ $\"About$

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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.

\n" ); document.write( "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.

\n" ); document.write( "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.

\n" ); document.write( "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.

\n" ); document.write( "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. \n" ); document.write( "

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