Question

A farmer has a fence of length 176 meter . He wants to use this fence around the area of his farm in such a way that the given fence(176m) cover maximum area of farm, in mathematical language he wants cover maximum area with fixed perimeter . for this he has to choose a specific shape of area around which fencing should be done


Q.1) what should be the shape of the area he choose ?



(A) rectangle



(B) square



(C) parallelogram



(D) circle

Q2)which of the following will be the area in meter square of the chosen area ?



(A) 2284



(B) 2000



(C) 2464



(D)2144







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Answer 1

Answer:

1.) For any shape with fixed perimeter, the shape with maximum number of sides will have maximum area, hence a circle has maximum area compared to any other shape.

Hence the farmer should use the shape of a (D) circle.

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2.)The fence is of length 176 m

Hence perimeter of the circle=176 m

To find the area of the circle we need the value of radius,we find it by     equating it to the perimeter and find the radius.

2πr=176 m {since perimeter of circle=2πr}

putting value of π=22/7

r=$\frac{176*7}{2*22}$

r=28 m

Area of a circle= πr²

                        =$\frac{22}{7}$×(28)²

                        =22×4×28

                        =2464m²

Hence the area of the farm will be  (C) 2464 m²

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Hope its clear!!

Answer 2

Answer:

1=circle

2= 2464..............