Question

Construct a triangle XYZ in which $\angle Y={30}^{\circ },\angle Z={90}^{\circ }andXY+YZ+ZX=11.$

Answer 1

Steps of construction :

(i) Draw a line segment PQ = 11 cm.

(ii) At P, draw a ray PL making an angle of ${30}^{\circ }$ and Q, draw another ray QM making an angle of ${90}^{\circ }$.

(iii) Draw the angle bisector of $\angle Pand\angle Q$ intersecting each other at X.

(iv) Draw the perpendicular bisector of XP and XQ which intersect PQ at Y and Z respectively.

(v) Join XY and XZ.

Then $△$XYZ is the required triangle.