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Mathematics

Assertion (A): Δ ABC ≅ Δ PQR

If 2AB = 3BC = 4CA = 12 cm, then the sum of perimeter of both triangle is 26 cm.

Reason (R): If two triangles are congruent to each other, then their corresponding sides are equal in length.

  1. Assertion (A) is true, Reason (R) is false.

  2. Assertion (A) is false, Reason (R) is true.

  3. Both Assertion (A) and Reason (R) are true, and Reason (R) is the correct reason for Assertion (A).

  4. Both Assertion (A) and Reason (R) are true, but Reason (R) is not the correct reason (or explanation) for Assertion (A).

Triangles

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Answer

When two triangles are congruent to each other, then their corresponding sides are equal in length.

It is a fundamental property of congruent triangles, better known as C.P.C.T.C.

∴ Reason (R) is true.

Given,

△ABC ≅ △PQR.

If 2AB = 3BC = 4CA = 12 cm.

For side AB, 2AB = 12 cm ⇒ AB = 122\dfrac{12}{2} = 6 cm,

For side BC, 3BC = 12 cm ⇒ BC = 123\dfrac{12}{3} = 4 cm,

For side CA, 4CA = 12 cm ⇒ CA = 124\dfrac{12}{4} = 3 cm.

Perimeter of △ABC = AB + BC + CA = 6 cm + 4 cm + 3 cm = 13 cm.

Since, △ABC ≅ △PQR their perimeters are equal.

Perimeter of △PQR = Perimeter of △ABC = 13 cm.

The sum of the perimeters of both triangles = Perimeter of △ABC + Perimeter of △PQR = 13 cm + 13 cm = 26 cm.

∴ Assertion (A) is true.

∴ Both Assertion (A) and Reason (R) are true, and Reason (R) is the correct reason (or explanation) for Assertion (A).

Hence, option 3 is the correct option.

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