In a triangle ABC the length of side BC is 295. If the length of side AB is a perfect square, then the length of side AC is a power of 2, and the length of side AC is twice the length of side AB. Determine the perimeter of the triangle.
Explanation:
2x2 is a power of 2.
Hence, x2 is a power of 2.
Hence, x is a power of 2.
Also by triangle inequality 3x2 > 295
∴ x2 > 98.33
∴ x ≥ 10
Hence, x is a power of 2 which is greater than 10.
We try with x = 16. Then we have,
AB = 256, AC = 512
∴ Perimeter = 256 + 512 +295= 1063, which is there in the options.
Hence, option (c).
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