Question

In a triangle ABC the length of side BC is
295 cm. 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
(in cm) of the triangle.
[IIFT - 2010]
(1) 343
(2) 487
(3) 1063
(4) None of these​

Answer 1

1063 cm is the perimeter of the triangle.

Step-by-step explanation:

Let,

Length of side AB = $2^{k - 1}$

so,

Length of side AC = $2^{k}$   (∵length of side AC is power of 2 and twice the  length of side AB)

Given that,

BC = 295 cm

Now,

The power of 2 that would fulfill these condition would be;

256 and 512,

AB = 256  (2^8(9 -1))

AC = 256 * 2 = 512     (256 is 2^9)

∵ The perimeter of the triangle = sum of all sides

= 256 + 295 + 512

= 1063 cm

Thus, 1063 cm is the perimeter of the triangle.

Learn more: Perimeter of the Triangle

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