IIFT 5th Dec 2021 Slot 1 Question 4

Question 4

A triangular park named ABC, is required to be protected by green fencing. The length of the side BC is 293. If the length of side AB is a perfect square, the length of the side AC is a power of two (2), and the length of side AC is twice the length of side AB. Determine how much fencing is required to cover the triangular park.

Solution

ABC is a triangle and BC =  293 
Let the length of AB = $$x^2$$
The length of AC = $$2^y$$
AC = 2AB
$$2^y = 2.x^2$$
$$2^{y-1} = x^2$$
$$2^{y-1}$$ is a perfect square when y is odd.
Sum of any two sides of a triangle should be larger than the third side. Therefore,
$$2^y + x^2$$ > 293, 293 + $$2^y$$ > $$x^2$$ and 293 + $$x^2$$ > $$2^y$$
y > 8
If y = 9, AC = 512, x = 16; satisfies above equations.
If y = 11, AC = 2048, x = 32; doesn't satisfy above equations.
Therefore, AB = 256 and AC = 512
Fencing required = 256 + 512 + 293 = 1061
Answer is option D.



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