Construct a triangle ABC in which BC = 4.7 cm, AB + AC = 8.2 cm and ∠C = 60°.

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asked Dec 29, 2017 in Class IX Maths by saurav24 Expert (1,431 points)
Construct a triangle ABC in which BC = 4.7 cm, AB + AC = 8.2 cm and ∠C = 60°.

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answered Dec 29, 2017 by navnit40 (-4,746 points)

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 

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