Statement A (Assertion) : ABC DEF such that ar( )=100 cm ^2 and a… - Vidyadip

MCQ

Statement $A ($Assertion$) : \triangle \text{ABC} \sim \triangle \text{DEF}$ such that $\operatorname{ar}(\triangle\text{ABC})=100 \ cm ^2$ and $\operatorname{ar}(\triangle \text{DEF})$
$=144 \ cm ^2$. If $A B=24 \ cm$, then $D E=36 \ cm$.
Statement $R ($Reason$) :$ The ratio of the areas of two similar triangles is equal to the ratio of the squares of their corresponding medians.

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 $(A).$
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.

Clearly, Reason is true.
Now, we know that, ratio of area of two similar triangles is equal to the ratio of squares of their corresponding sides.
$\therefore \frac{\operatorname{ar}(\triangle A B C)}{\operatorname{ar}(\triangle D E F)}=\frac{A B^2}{D E^2}$
$\Rightarrow \frac{100}{144}=\frac{24 \times 24}{D E^2}$
$\Rightarrow D E^2=\frac{24 \times 24 \times 144}{100}$
$\Rightarrow D E=\frac{24 \times 12}{10}=\frac{288}{10}$
$=28.8 \neq 36$
$\therefore$ Assertion is false.

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