Question

Construct ΔXYZ, if its perimeter is 14 cm, one side XY of length 5 cm and ∠X= 45°.

Answer 1

Here, perimeter of ΔXYZ = 14 cm and one side XY = 5 cm
YZ + XZ = 14 – 5 = 9 cm and ∠X = 45°.
Steps of construction :

1. Draw a line segment XY = 5 cm.
2. Construct an angle ∠YXA = 45° with the help of compass and ruler.
3. From ray XA, cut off XB = 9 cm.
4. Join BY.
5. Draw perpendicular bisector of BY and let it intersect XB in Z.
6. Join ZY. Thus, ΔXYZ is the required triangle.