Direction : In the following questions, a statement of assertion … - Vidyadip

MCQ

Direction : In the following questions, a statement of assertion $(A)$ is followed by a statement of reason $(R)$. Mark the correct choice as:
Assertion : $D$ and $E$ are points on the sides $AB $ and $AC$ respectively of a $\triangle\text{ABC}$ such that $AD = 5.7\ cm, DB = 9.5\ cm, AE = 4.8\ cm$ and $EC = 8\ cm$ then $DE$ isnot parallel to $BC.$
Reason : If a line divides any two sides of a triangle in the same ratio then it is parallel to the third side.

A
Both assertion $(A)$ and reason $(R)$ are true and reason $(R)$ isthe correct explanation of assertion $(A)$.
B
Both assertion $(A)$ and reason $(R)$ are true but reason $(R)$ is not the correct explanation of assertion $(A)$.
C
Assertion $(A)$ is true but reason $(R)$ is false.
✓
Assertion $(A)$ is false but reason $(R)$ is true.

✓

Answer

Correct option: D.

Assertion $(A)$ is false but reason $(R)$ is true.

If a line divides any two sides of a triangle in the same ratio then it is parallel to the third side.
This is Converse of Basic Proportionality theorem.
So, Reason is correct.

Now, $ \frac{\text{AD}}{\text{DB}}=\frac{5.7}{9.5}=\frac{57}{95}=\frac{3}{5}$
and $ \frac{\text{AE}}{\text{EC}}=\frac{4.8}{8}=\frac{48}{8}=\frac{3}{5}$
$\Rightarrow\frac{\text{AD}}{\text{DB}}=\frac{\text{AE}}{\text{EC}}$
By Converse of Basic Proportionality theorem, $DE \| BC$
So, Assertion is not correct.

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