Question

construct an triangle xyz in which angle Y =30° angle Z=90° and XY+YZ+ZX =11cm

Answer 1

Draw a line segment AB of 11 cm 
Construct 30° from A and 90° from B
Construct angle bisectors for both the angles 
They will meet at X
Construct  perpendicular line bisector for  AX and BX .
The both lines will meet AB at X and Y
Join XY and XZ 
XYZ is our required triangle.

Answer 2

Step 1: A line segment AB= 11 cm is drawn. (XY + YZ + ZX = 11 cm)
Step 2: An angle, ∠A= 30° is constructed at point A and an angle ∠B = 90° at point B.
Step 3: ∠A and ∠B are bisected . The bisectors of these angles intersect each other at point X.
Step 4: Perpendicular bisectors TS of AX and ZU of BX are constructed.
Step V: Let TS intersect ABat Y and ZU intersect AB at Z. XY and XZ are joined.
Thus, ΔXYZ is the required triangle.