Steps of Construction:
1. Draw a line segment AB = 11 cm (XY + YZ + ZX= 11 cm)
2. Construct an angle of 30° at the point A.
3. Construct an angle of 90° at the point B.
4. Bisect these two angles at A and B respectively and let their bisectors meet at the point X.
5. Draw a perpendicular bisector CD of AX and EF of XB to intersect AB at point Y and Z respectively. Join X, Y and X, Z.
Thus, ∆XYZ is the required triangle.
Verification: Measure the sides XY, YZ and ZX of ∆XYZ. It is found that XY + YZ + ZX= 11 cm.