(a) Steps of constructions, when m < n:

Step I. Construct the given triangle ABC by using the given data.

Step II. Take any one of the three sides of the given triangle as base. Let AB be the base of the given triangle.

step III. At one end, say A, of base AB. Construct an acute ∠BAX below the base AB.

Step IV.  Along AX mark off n points A₁,A₂,A₃,..............,An such that AA₁ = A₁A₂ = ........... = A_n-1A_n.   

Step V. Join An B.

Step VI. Draw A_mB' parallel to A_nB which meets, AB at B'.

Step VII. From B' draw B'C' || CB meeting AC at C'.

Triangle AB'C' is the required triangle each of whose sides is (m/n) ^th of the corresponding side of ΔABC.

(b) Steps of construction when m > n:

Step I. Construct the given triangle by using the given data.

Step II. Take any one of the three sides of the given triangle and consider it as the base. Let AB be the base of the given triangle.

Step III. At one end, say A, of base AB. Construct an acute angle ∠BAX below the base AB i.e., on the opposite side of the vertex C.

Step IV. Along AX mark off m (larger of m and n) points A₁,A₂,A₃,............A_m such that AA₁ = A₁A₂ = ............. = A_m-1A_m.

Step V. Join A_nB to B and draw a line through A. parallel to A_nB, intersecting the extended line segment AB at B'.

Step VI. Draw a line through B' parallel to BC intersecting the extended line segment AC at C'.

ΔAB'C' so obtained is the required triangle.