Question

Assertion (A): If $$\triangle ABC\sim\triangle DEF$$ such that $$2AB = 3DE$$ and $$BC = 6\ \text{cm}$$ then $$EF = 4\ \text{cm}$$.

Reason (R): The corresponding sides of similar triangles are proportional.

Options

• Both Assertion (A) and Reason (R) are true and Reason (R) is a correct explanation of Assertion (A).

• Both Assertion (A) and Reason (R) are true but Reason (R) is not a correct explanation of Assertion (A).

• Assertion (A) is true and Reason (R) is false.

• Assertion (A) is false and Reason (R) is true.

Answer 1

Both Assertion (A) and Reason (R) are true and Reason (R) is a correct explanation of Assertion (A).

Explanation:

Step 1 – Assertion: A is true. From $$2AB=3DE$$, we get $$\frac{AB}{DE}=\frac{3}{2}$$. Similarity gives $$\frac{BC}{EF}=\frac{3}{2}$$, so $$\frac{6}{EF}=\frac{3}{2}$$ and $$EF=4\ \text{cm}$$.

Step 2 – Reason: R is true. Corresponding sides of similar triangles are proportional.

Step 3 – Link: Applying the proportionality of corresponding sides gives the stated value of $$EF$$.