Question

Directions: In the following questions, a statement of Assertion (A) is followed by a statement of Reason (R).
Mark the correct choice as:

Assertion (A): D and E are points on the sides AB and AC respectively of a ΔABC such that DE║BC then the value of $a$ is 8, when AD = $a$ cm, DB = $(a-4)$ cm, AE = $(a+4)$ cm and EC = $(a-2)$ cm.

Reason (R): If a line is parallel to one side of a triangle then it divides the other two sides in the same ratio .

• A. Both Assertion (A) and Reason (R) are true, and Reason (R) is the correct explanation of Assertion (A).
• B. Assertion (A) is false, but Reason (R) is true.
• C. Both Assertion (A) and Reason (R) are true, but Reason (R) is not the correct explanation of Assertion (A).
• D. Assertion (A) is true, but Reason (R) is false.

Answer 1

The correct option is A Both Assertion (A) and Reason (R) are true, and Reason (R) is the correct explanation of Assertion (A).

From image we can see that, D and E are points on the sides AB and AC respectively of a ΔABC and DE is parallel to BC.

Also,

→ AD = a cm

→ DB = (a - 4) cm

→ AE = (a + 4) cm

→ EC = (a - 2) cm

Now, since DE || BC .

→ $\frac{AD}{DB}=\frac{AE}{EC}$ {If a line is parallel to one side of a triangle then it divides the other two sides in the same ratio}

→ $\frac{a}{a-4}=\frac{a+4}{a-2}$

→ $a²-2a=\left(a\right)²-\left(4\right)²$

→ $a²-2a=a²-16$

→ $(-2a)=(-16)$

→ $a=8$

Therefore, value of $a$ is equal to 8 .

Conclusion :-

• Assertion (A) is true .
• Reason (R) is true .
• Reason (R) is the correct explanation of assertion (A).

Hence, Option (a) is correct answer.