Question

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

Answer 1

Construct a triangle XYZ in which ∠Y = 30° , ∠Z = 90° and XY+YZ+ZX = 11 cm 

The steps explained below will be followed to construct the required triangle 

 

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 90° at point B 

Step 3: Bisect ∠PAB and ∠QBA let theses intersect 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 

Join XY, XZ 

ΔXYZ is the required triangle