Statement A (Assertion) : In two similar triangles A B C and P Q … - Vidyadip

MCQ

Statement A (Assertion) : In two similar triangles $A B C$ and $P Q R$, if their corresponding altitudes $A D$ and $P S$ are in the ratio $4: 9$, then the ratio of the areas of $\triangle A B C$ and $\triangle P Q R$ is $16: 81$.
Statement R (Reason) : The ratio of the areas of two similar triangles is equal to the ratio of their corresponding altitudes.

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

✓

Answer

Correct option: C.

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

(c) : Clearly, Reason is false.
Since the ratio of areas of two similar triangles is equal to the ratio of the squares of their corresponding altitudes.
$
\therefore \quad \frac{\operatorname{ar}(\triangle A B C)}{\operatorname{ar}(\triangle P Q R)}=\frac{A D^2}{P S^2}=\left(\frac{4}{9}\right)^2=\frac{16}{81}
$
$\therefore \quad$ Assertion is true.

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