Construct a triangle XYZ in which angle Y= 30degree, angle Z = 90degree and XY+YZ+ZX=11cm.

Step 1: 

Draw a line segment AB of 11 cm.

(As XY + YZ + ZX = 11 cm)

Step 2: 

Construct an angle, ∠PAB, of 30� at point A and an angle, ∠QBA, of 90degree at point B.

Step 3: 

Bisect ∠PAB and ∠QBA. Let these bisectors intersect each other at point X.

Step 4: 

Draw perpendicular bisector ST of AX and UV of BX.

Step 5:

Let ST intersect AB at Y and UV intersect AB at Z.

Step 6:

Join XY, XZ.

Thus, ΔXYZ is the required triangle.