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Mathematics

Assertion (A): When each side of a square is increased by 5 cm, its area increases by 75 sq. cm. The side of the square is 5 cm.

Reason (R):

When each side of a square is increased by 5 cm, its area increases by 75 sq. cm. The side of the square is 5 cm. Assertion Reasoning, Concise Mathematics Solutions ICSE Class 9.

⇒ (x+5)2 = x2 + 75 ⇒ x = 5cm

  1. A is true, R is false.
  2. A is false, R is true.
  3. Both A and R are true.
  4. Both A and R are false.

Mensuration

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Answer

Both A and R are true.

Explanation

Let x be the side of square.

Area of square = x2

Side of square is increased by 5 cm, new side = x + 5

New area = x2 + 75 sq. cm

⇒ (x + 5)2 = x2 + 75

⇒ x2 + 52 + 2 ×\times x ×\times 5 = x2 + 75

⇒ x2 + 25 + 10x = x2 + 75

⇒ 25 + 10x - 75 = 0

⇒ 10x - 50 = 0

⇒ 10x = 50

⇒ x = 5010\dfrac{50}{10}

⇒ x = 5

∴ Assertion (A) is true.

From the above calculations,

x = 5cm

∴ Reason (R) is true.

Hence, both Assertion (A) and Reason (R) are true.

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