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