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Solution


Q.

In the given triangle (Right angled at C), DE || BC, AB = 5 cm, AD = 2 cm and BC = 3 cm. Using BPT/Thales theorem:

                             

(i) AE = 8/5 cm

(ii) AE = 1 cm

(iii) AC = 4 cm

(iv) AC = 3 cm

Choose the correct option from the following:
1 (i) and (iii) are correct.  
2 (i) and (iv) are correct.  
3 (ii) and (iii) are correct.  
4 (ii) and (iv) are correct  

Ans.

(1)

Given right angled triangle ABC, using Pythagoras theorem we have

AB² = AC² + BC² ⇒ 5² = AC² + 9 ⇒ AC² = 25 – 9 = 16 ⇒ AC = 4 cm, Hence (iii) is correct.Given DE ∥ BC, using BPT theorem,AD/AB = AE/AC ⇒ 2/5 = AE/4⇒ AE = 8/5 cm, Hence (i) is correct.