Question

No.8 (15 points) The Texae highway department is planning to build a rectangular picnic area for motorists along a major highway. It is to be fenced off on the three sides not adjacent to the the highway with a moot 200 meters of fencing, What are the dimensions of the rectangular picnic area that will produce the largest Ares 7 What is this largest area? Hint: Draw a picture to help you understand the problem.

Answer 1

A CA Y Length of the fencing, L= 200. " x txty a 200 iant y = 200 .: Y = 200 -23 Area of the rectangle pícnic area = ny. A = n( 200-22) A = 2001 - 202 for the Area to be largent, A'(x) = 0 A(x) = 200-40=0 => 200 = 427 X= 200 = 50 meter Al(x) = -420 . Area is maximum at x = 50m ..y= 200- (2x50) = 200-100 Y = 100ml . The Largent Area = XY - 50x100 = 5000 m2