Construct a triangle XYZ in which  angleY = 30 degree, angle Z = 90 degree, xy + yz + zx = 11cm.
.Is it possible to  have a triangle like this without decimals considering the Pythagorean theorem??

Step I: Draw a line segment AB of 11 cm.

(As XY + YZ + ZX = 11 cm)

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

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

Step IV: Draw perpendicular bisector ST of AX and UV of BX.

Step V: Let ST intersect AB at Y and UV intersect AB at Z.

Join XY, XZ.

ΔXYZ is the required triangle