Question

Assertion :$△ABC$ and $△DEF$ are two similar triangles such that $BC=4$ cm, $EF=5$ cm and $A\left(△ABC\right)=64c{m}^2$, then $A\left(△DEF\right)=100c{m}^2$. Reason: The areas of two similar triangles are in the ratio of the squares of the corresponding altitudes.

• A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion.
• B. Both Assertion and Reason are correct, but Reason is not the correct explanation for Assertion.
• C. Assertion is correct but Reason is incorrect.
• D. Assertion is incorrect but Reason is correct.

Answer 1

The correct option is B Both Assertion and Reason are correct, but Reason is not the correct explanation for Assertion.

Reason is true .... [$\because$ of standard result]

For Assertion, since $△ABC\sim △DEF$

$\therefore \frac{A\left(△ABC\right)}{A\left(△DEF\right)}=\frac{B{C}^2}{E{F}^2}=\frac{(4{)}^2}{(5{)}^2}=\frac{16}{25}$
($\because$ ratio of areas of two similar $△s$ is equal to the ratio of the squares of corresponding sides)

$\therefore \frac{64}{A\left(△DEF\right)}=\frac{16}{25}\Rightarrow A\left(△DEF\right)=\frac{64\times 25}{16}$

$=4\times 25=100c{m}^2$

$\therefore$ Assertion is true. But Reason is not the correct explanation for Assertion.