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Mathematics

Assertion (A): Perimeter of a garden is 24 cm, while the difference between its length and width is 2 units. Then its area is 35 sq. cm.

Reason (R): If length of a rectangle is doubled, while width remains the same, then the perimeter also gets doubled.

  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).

Linear Equations

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Answer

Let l cm be the length of a garden and b cm be the width of the garden.

Given,

Difference between length and width is 2 units.

⇒ l - b = 2

⇒ l = 2 + b ……….(1)

Given,

Perimeter = 24 cm

⇒ 2(l + b) = 24 cm

⇒ 2[2 + b + b] = 24     [From equation (1)]

⇒ 2(2b + 2) = 24

⇒ 4b + 4 = 24

⇒ 4b = 24 - 4

⇒ 4b = 20

⇒ b = 204\dfrac{20}{4}

⇒ b = 5 cm.

The length of a garden (l) = 2 + b = 2 + 5 = 7 cm.

Area of garden = l x b

= 7 x 5 sq. cm.

= 35 sq. cm.

∴ Assertion (A) is true.

Length of a rectangle is doubled, while width remains the same.

⇒ New length = 2l and New width = b

New perimeter = 2(New length + New width)

= 2(2l + b)

So, the perimeter does not gets double.

∴ Reason (R) is false.

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

Hence, option 1 is the correct option.

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