Construct a ΔABC such that AB = 6.5 cm, AC = 5 cm and the altitude AP to BC is 4 cm.

 

Steps of construction:

(i) Draw a line l and take any point P on it.

(ii) Construct a perpendicular to l at P.

(iii) Cut AP = 4 cm.

(iv) Draw two arcs with centre A and radii 6.5 cm and 5 cm to cut the line l at B and C respectively.

(v) Join AB and AC.

(vi) ΔABC is the required triangle.