The rectangular bird sanctuary with one side along a straight river is to be constructed so that it contains 8 km2 of area. Find the dimen - sions of the rectangle to minimize the amount of fence necessary to enclose the remaining three sides.

Question

Wilson Frederick

Mathematics

14 July, 15:43

The rectangular bird sanctuary with one side along a straight river is to be constructed so that it contains 8 km2 of area. Find the dimen - sions of the rectangle to minimize the amount of fence necessary to enclose the remaining three sides.

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Answers (1)

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Antony Solis · Answer 1

Given:

Rectangular enclosure w / area of 8km²

Area = length * width

Solve for perimeter of 3 sides only. The river will serve as the 4th side of the enclosure.

Possible dimensions:

8 = 8 x 1; P = 8 + 1 + 1 = 10 km.

8 = 4 x 2; P = 4 + 2 + 2 = 8 km.

Best dimension is length of 4 km and width of 2 km. The river will serve as the other length. It will only need 8 km of fence to enclose the area 8 km².