Solution:

This question took me around 5 mins to crack. For me, it's definitely not an easy one.

So, as we know the smallest angles is 45 and the sum of all angles of triangle=180.
Thus, the other 2 angles should have a sum of 180-45=135

Therefore, the \(\frac{ratio of the two sides}{ smallest side}=\frac{135}{45}=\frac{3}{1}
\)
From the above ratio, the sides of the triangles will also be in the same ratio.

For eg. consider option A: the smallest side has to be 2 and the sum of other two sides=6
Thus , the ratio will be\( \frac{6}{2}=\frac{3}{1}
\)
Similarly when we try for other options, Option B and D satisfies the condition

IMO A, B & D

Hope this helps

A. \(2x + 3x + 3x = 180\)
\(x = \frac{180}{8} = 22.5\)
22.5 x 2 = 45

B. \(3x + 4x + 5x = 180\)
\(x = \frac{180}{12} = 15\)
15 x 3 = 45

C. \(3x + 5x + 7x = 180\)
\(x = \frac{180}{15} = 12\)
Cannot make 45

D. \(9x + 10x + 17x = 180\)
\(x = \frac{180}{36} = 5\)
9 x 5 = 45

E. \(9x + 11x + 13x = 180\)
\(x = \frac{180}{33} = 5.45\)
Cannot make 45

F. \(15x + 17x + 18x = 180\)
\(x = \frac{180}{8} = 3.6\)
Cannot make 45

Hence, A, B and D

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