Statement A (Assertion) : In the given figure, if D E | A C, then… - Vidyadip

MCQ

Statement A (Assertion) : In the given figure, if $D E \| A C$, then, the value of $x$ is 1 .

Statement $R$ (Reason) : A line segment dividing the two sides of a triangle in same ratio is parallel to third side.

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

✓

Answer

Correct option: A.

Both assertion (A) and reason ( $R$ ) are true and reason $(R)$ is the correct explanation of assertion $(A)$.

(a): In $\triangle A B C, D E \| A C$
$
\begin{array}{ll}
\therefore & \frac{B D}{A D}=\frac{B E}{E C} [By\quad B.P.T]\\
\Rightarrow & \frac{2 x+10}{3 x}=\frac{x+7}{2 x} \\
\Rightarrow & 4 x^2+20 x=3 x^2+21 x \Rightarrow x^2-x=0 \\
\Rightarrow & x(x-1)=0 \\
\Rightarrow & x=1\quad\quad [ \therefore Side\quad can't\quad be\quad zero]
\end{array}
$
$\therefore \quad$ Assertion is true.
Clearly, Reason is true.
$\therefore \quad$ Assertion and Reason both are true and Reason is the correct explanation of Assertion.

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