Solution
Steps of construction:
1. Draw AB = 5.8 cm and ∠ABX = 60°.
2. Cut BD = 7 cm along BX.
3. Join AD and draw PQ, ⊥ bisector of AD.
4. PQ intersects AD at L and BD at C.
5. Join AC.
Hence, ΔABC is the required triangle.
Justification:
We observe that in ΔCAD, CL is perpendicular bisector of AD.
⇒ CA = CD
⇒ BC + CA = BC + CD = BD = 7 cm.
