1. 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.
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By: anil on 05 May 2019 02.40 am
Let AC = $$2^k$$
AC = 2 * AB
So, AB = $$2^{k - 1}$$
Only 256 and 512 satisfy this condition as the third side is 295 and we have to ensure that sum of the two sides of the triangle is greater than the third side.
Thus, the perimeter = (256 + 512 + 295) = 1063.
Hence, option C is the correct answer.
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AC = 2 * AB
So, AB = $$2^{k - 1}$$
Only 256 and 512 satisfy this condition as the third side is 295 and we have to ensure that sum of the two sides of the triangle is greater than the third side.
Thus, the perimeter = (256 + 512 + 295) = 1063.
Hence, option C is the correct answer.