Framer has 2000 ft fencing and wants fence off rectangular field that borders a straight river

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Suresh Chand · Accepted Answer

Solution: Let A be the area of rectangular field. Suppose x and y are width and length of rectangle field, so A = xy   Also 2x + y   = 2400 y = 2400 - 2x Thus A = x(2400 - 2x) (A = 2400 - 2x^{2}) Now, (A^{ˈ} = 2400 - 4x) For A is maximum, (A^{ˈ} = 0) (therefore 2400 - 4x = 0) i.e. x = 600 Again, (A^{ˈˈ} = - 4 < 0) Therefore, A is maximum when x = 600 ft and y = 2400 - 2 x 600 = 1200 ft. Therefore, Length of rectangular field is 1200 ft and width is 600 ft, so that 2400 ft fencing enclosed maximum area.

A farmer has 2000 ft of fencing and wants to fence off a rectangular field that borders a straight river. He needs no fence along the river. What are the dimensions of the field that has the largest area?

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A farmer has 2000 ft of fencing and wants to fence off a rectangular field that borders a straight river. He needs no fence along the river. What are the dimensions of the field that has the largest area?

Leave your Answer: