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13 May 2020, 20:28
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A
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Difficulty:
45%
(medium)
Question Stats:
70% (02:26) correct
30%
(02:45)
wrong
based on 253
sessions
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There is a square field of side 500 m long each. It has a compound wall along its perimeter. At one
of its corners, a triangular area of the field is to be cordoned off by erecting a straight-line fence. The
compound wall and the fence will form its borders. If the length of the fence is 100 m, what is the
maximum area that can be cordoned off?
A. 2,500 sq m
B. 10,000 sq m
C. 5,000 sq m
D. 20,000 sq m
E. 7,500 sq m
of its corners, a triangular area of the field is to be cordoned off by erecting a straight-line fence. The
compound wall and the fence will form its borders. If the length of the fence is 100 m, what is the
maximum area that can be cordoned off?
A. 2,500 sq m
B. 10,000 sq m
C. 5,000 sq m
D. 20,000 sq m
E. 7,500 sq m
13 May 2020, 20:45
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We need to find out maximum possible area of the triangle formed by the walls(as the triangle's sides at a right angle) and the fence (as its hypotenuse).
Fence is 100 m
The other two side will definitely be less than 100m each
The area of triangle will definitely be less than 1/2(100*100)
Area of triangle < 1/2(100*100)
Area of triangle < 100*50
Area of triangle < 5000
The only option less than 5000 is 2500, Option A
Fence is 100 m
The other two side will definitely be less than 100m each
The area of triangle will definitely be less than 1/2(100*100)
Area of triangle < 1/2(100*100)
Area of triangle < 100*50
Area of triangle < 5000
The only option less than 5000 is 2500, Option A
13 May 2020, 21:06
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preetamsaha
Method:
CONCEPT: For a right triangle with given Hypotenuse, the area of triangle is maximum when two legs are equal
i.e. Fence of 100 m will serve the purpose of hypotenuse of a right triangluar corner
i.e. Sides of triangular corner = 100/√2 = 50√2 each
Area of Triangles = (1/2)*50√2*50√2 = 2500
Answer: Option A
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