Assertion (A): In Fig. 6.78, \triangle ABC\sim\triangle AED. If BC = 8 cm, AB = 6.5 cm, AD = 2.8 cm and DE = 4

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Q.
$A s s e r t i o n (A) : I n F i g . ∆ A B C ~ ∆ A E D . I f B C = 8 c m, A B = 6.5 c m, A D = 2.8 c m a n d D E = 4 c m, t h e n A C = 5.6 cm$

Reason (R): If in two triangles, angles of one triangle are proportional to the angles of the other triangle, then their corresponding sides are equal, and hence, the two triangles are similar.

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.
(3)

$G i v e n, ∆ A B C ~ ∆ A E D$

$W e h a v e : B C = 8 c m, A B = 6.5 c m, A D = 2.8 c m, D E = 4 c m .$

$N o w, \frac{A B}{A E} = \frac{B C}{E D} = \frac{A C}{A D} (∵ ∆ A B C ~ ∆ A E D)$

$F r o m \frac{B C}{E D} = \frac{A C}{A D} \Rightarrow \frac{8}{4} = \frac{A C}{2.8}$

$2 \times 2.8 = A C C = 5.6 cm$

Solution

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

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Solution

Q. Assertion(A):In Fig. ∆ABC~∆AED.If BC=8cm, AB=6.5cm, AD=2.8cm and DE=4cm, then AC=5.6 cm Reason (R): If in two triangles, angles of one triangle are proportional to the angles of the other triangle, then their corresponding sides are equal, and hence, the two triangles are similar.

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. (3) Given,∆ABC~∆AED We have: BC = 8 cm, AB = 6.5 cm, AD = 2.8 cm, DE = 4 cm. Now,ABAE=BCED=ACAD(∵∆ABC~∆AED) FromBCED=ACAD⇒84=AC2.8 2×2.8=ACC=5.6 cm

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