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Solution


Q.

In the given triangle, we have AB = 12 cm, AC = 13 cm, AE = 13/4 cm, BC = 5 cm and AD = 3 cm. Then:

(i) ABC is a right-angled triangle

(ii) DE is parallel to BC

(iii) ABC is not a right-angled triangle

(iv) DE is perpendicular to AB

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

Ans.

(4)

Checking for right-angled triangle:

Given, AB = 12 cm, BC = 5 cm and AC = 13 cm(AB)² + (BC)² = (12)² + (5)² = 144 + 25 = 169 = (13)²So, (AB)² + (BC)² = (AC)², by Pythagoras Theorem,ΔABC is right angled at B.Hence, (i) is correct, and (iii) is incorrectNow, AD/AB = 3/12 = 1/4 and AE/AC = (13/4 × 1/13) = 1/4By BPT if AD/AB = AE/AC, then DE ∥ BC, Hence (ii) is correct.As B is a right angle and DE ∥ BC, angle D will also be 90°, so DE ⟂ AB,Hence (iv) is correct.