There is a square field of side 500 m long each. It has a compound wal

Question

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

Shrey08 · Answer

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

GMATinsight · Answer

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

jcerdae · Answer

Hi!
Thank you for the picture! It truly helped me to solve the problem. BUT!! its been the second time where I try to do the excersice by myself (after forgetting how to solve it) and still fail on how to draw it correctly!

Where does it say that the square loses a triangular area?? Thank you in advanced!

stne · Answer

Hi  jcerdae ,

In the question it says "At one of its corners, a  triangular area  of the field is to be cordoned off by erecting a straight-line fence. The perimeter wall and the fence will form its borders"

This clearly means that in one  corner  of the square a triangle is formed, with a hypotenuse of 100. The legs of the triangle will be portions the perimeter wall.

Hope this helps.

jcerdae · Answer

Thank you so much  stne  !!!
It helped me!!!

ScottTargetTestPrep · Answer

Solution:

The maximum area that can be cordoned off is the area of a right isosceles triangle with the hypotenuse equal to the length of the fence. Since the length of the fence is 100 m, then a non-hypotenuse side of the triangle is 100 / √2 = 50√2 m, and the area of the triangle is ½ x 50√2 x 50√2 = 2500 sq m.

Answer: A

Logo · Answer

How come you can't use a^2+b^2=c^2 on this problem?

bumpbot · Answer

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There is a square field of side 500 m long each. It has a compound wal

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There is a square field of side 500 m long each. It has a compound wal

Prep Toolkit

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