Is it mandatory to write down the steps of construction and the justification,even if it isn't mentioned in the question ?If so, please provide me with a brief explation of what is meant by justification of construction with an example.
It is mandatory to write the steps of construction every time you construct a geometric figure. But, justification is written only when it is asked in the question.
Here, is an example of construction of triangle similar to the given triangle with sides 
of the sides of given triangle.
Consider, the triangle PQR.
Following are the steps of construction:
1) Firstly, we draw a ray QX making an acute angle with QR on the side opposite to vertex P and Mark 3 points (corresponding to the greater of 2 or 3) X1, X2, X3 on Q × such that QX1 =X1X2 = X2X3.
2) Now, we join X2R (corresponding to the denominator of the given ratio) and draw a line passing through X3 (corresponding to the numerator of the given ratio) and parallel to X2R. Let this intersect the extended line QR at point R´.
3) Now, we draw a line passing through R´ and parallel to RP, which intersects the extended line PQ at point P´.
4) Thus, P´QR´ is the required triangle which is similar to the given triangles and with sides of the sides of the given triangle.
Justification:
Consider ΔPQR and ΔP´QR´,
∠Q = ∠Q (common)
∠QRP = ∠QR´P´ (Corresponding angles, as P´R´|| PR)
∴ ΔPQR ∼ ΔP´QR´ (By AA similarity rule)
Similarly, ΔQRX2 ∼ ΔQR´ X3
Now, 
and, 
From equation (1) and (2),
Thus, ΔP´QR´ is similar to ΔPQR with sides of the sides of ΔPQR.