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.
Explanation:
ABC is a triangle and BC = 293 Let the length of AB = x2 The length of AC = 2y AC = 2AB
2y = 2.x2
2y - 1 = x2
2y - 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,
2y + x2 > 293, 293 + 2y > x2 and 293 + x2 > 2y
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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