Given : In ΔABC, BC= 4.7 cm, AB + AC = 8.2 cm and ∠C= 60°.
Required : To construct ΔABC.
Steps of construction:
1. Draw BC = 4.7 cm.
2. Draw ∠BCX
3. From ray CX, cut off CD = 8.2
4. Join BD.
5. Draw the perpendicular bisector of BD meeting CD at A.
6. Join AB to obtain the required triangle ABC.
Justification :
∵ A lies on the perpendicular bisector BD, therefore
AB = AD
Now, CD = 8.2 cm ⇒ AC + AD = 8.2 cm ⇒ AC + AB = 8.2 cm