Arectangular bird sanctuary is being created with one side along a straight riverbank. the remaining three sides are to be enclosed with a protective fence. if there are 28 km of fence available, find the dimension of the rectangle to maximize the area of the sanctuary.

  The rectangle is 7 km by 14 km. The 14 km dimension is parallel to the river.

Step-by-step explanation:

Let x represent the length of fence parallel to the river. The remaining fence is divided into two equal pieces for the ends of the enclosure. Then (28 -x)/2 will be the length of the side of the rectangle perpendicular to the river.

The total area of the enclosure is the product of length and width:

  Area = (x)(28-x)/2

This expression describes a parabola opening downward with zeros at x=0 and x=28. The vertex (maximum) is halfway between those zeros, so is at ...

  x = (0 +28)/2 = 14

Area is maximized when the dimension parallel to the river is 14 km and the ends of the enclosure are 7 km.

56.6

step-by-step explanation:

the ratio of the perimeters is equal to the scale.

the ratio of the areas is equal to the square of the scale.

34 / 20 = k

a / 19.6 = k²

substituting:

a / 19.6 = (34 / 20)²

a = 19.6 (34 / 20)²

a ≈ 56.6

answer: 140

step-by-step explanation:

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