Question

Assertion (A): Two sides and the perimeter of one triangle are respectively three times the corresponding sides and the perimeter of the other triangle. Then, the two triangles are similar.

Reason (R): If all the three corresponding sides of two triangles are proportional then the triangles are similar.

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. If two corresponding sides of one triangle are three times those of the other and the same is true for the perimeters, subtracting the two known sides from each perimeter shows that the third corresponding sides are also in the ratio $$3:1$$.

Step 2 – Reason: R is true. If all three pairs of corresponding sides are proportional, the triangles are similar by the SSS criterion.

Step 3 – Link: The perimeter condition establishes the same proportionality for the third pair of sides; therefore, R explains the similarity asserted.