Jim and Martha are standing together at the corner of a rectangular field. Jim walks diagonally across the field. Martha gets to the same location by walking along its length and width. The field is 300 feet wide and 400 feet long. How many feet less than Martha does Jim walk?
I need to compare the distances that Jim and Martha walk, so I'll start by finding their respective distances. Jim walks diagonally across the field, so his distance is the hypotenuse of a right triangle with legs of 300 and 400 feet. I can use the Pythagorean theorem to find his distance: a^2 + b^2 = c^2, where a and b are the legs and c is the hypotenuse. Plugging in the given values, I get 300^2 + 400^2 = c^2, which simplifies to 250000 = c^2. To find c, I take the square root of both sides and get c = sqrt(250000) = 500 feet. So Jim walks 500 feet across the field. Martha walks along the length and width of the field, so her distance is the sum of those two dimensions: 300 + 400 = 700 feet. So Martha walks 700 feet around the field. To find how many feet less than Martha Jim walks, I subtract their distances: 700 - 500 = 200 feet. So Jim walks 200 feet less than Martha. 