A field in the shape of a right triangle (with the two shortest sides measuring 60 feet and 80 feet) has roads on all three sides that don't drain properly. As a result, muddy water puddles collect and when the cars pass through, they splash all the snow that is within 5 feet of any one of the three roads.

If all other snow not splashed by cars is kept clean, what percent is clean?

56.25%

Draw a triangle with the given side lengths(hypoteneuse is sqrt(60^2+80^2)=100). Since you know the clean area will be a similar triangle, you need only to find the length of one side of the clean area. To do this, either the side length 60 or 80 is easier. Subtract 5 from whatever side you choose. 60-5=55. Now draw a kite in the corner where side 60 meets side 100. In the kite, draw a rectangle from where the two 5's meet, and since the resultant triangles are similar to the original, 5 is equal to side length 80. 80/5=16. Divide 60 by 16 to get 3.75, 3.75+6.25=10, so side length 60 originally is now side length 45. 45/60=.75, and .75*80=60. 60*45/2= area of clean snow=1350 ft^2. 1350/(80*60/2)=1350/2400=.5625. 100%*.5625=56.25% of the area remains clean!

Posted by Justin on 2005-05-15 18:53:08