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Solution


Q.

Assertion (A): D and E are points on the sides AB and AC respectively of ΔABC such that AB = 10.8 cm, AD = 6.3 cm, AC = 9.6 cm, EC = 4 cm, then DE is parallel to BC.

Reason (R): If a line is parallel to one side, then it divides the other two sides in the same ratio
1 Both A and R are true, and R is the correct explanation of A.  
2 Both A and R are true, but R is not the correct explanation of A  
3 A is true, but R is false.  
4 A is false, but R is true.  

Ans.

(2)

In ΔABC, D and E are points on sides AB and AC respectively such that

AB = 10.8 cm, AD = 6.3 cm, AC = 9.6 cm, EC = 4 cm

BD=AB−AD=10.8−6.3=4.5 cmAE=AC−EC=9.6−4=5.6 cmNow, ADBD=6.34.5=6345=2115=75and   AEEC=5.64=5640=75⇒ADBD=AEEC⇒DE∥BC

Therefore, Assertion (A) is true, Reason (R) is also true, but Reason (R) is not the correct explanation of Assertion (A).