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Mathematics

Assertion (A): According to the information in the given figure, the length of BC = 10 cm.

According to the information in the given figure, the length of BC = 10 cm. Assertion Reasoning, Concise Mathematics Solutions ICSE Class 9.

Reason (R):

BC=132−122 cm=5 cm\text{BC} = \sqrt{13^2 - 12^2}\text{ cm} = 5\text{ cm}
AC=202−122 cm=16 cm\text{AC} = \sqrt{20^2 - 12^2}\text{ cm} = 16\text{ cm}
∴ AB = AC - BC = 11 cm

  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.

Pythagoras Theorem

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Answer

A is false, R is true.

Explanation

In Δ BPC, using Pythagoras Theorem,

BP2 = PC2 + BC2

⇒ 132 = 122 + BC2

⇒ 169 = 144 + BC2

⇒ BC2 = 169 - 144

⇒ BC2 = 25

⇒ BC = 25\sqrt{25}

⇒ BC = 5 cm

According to Assertion, BC = 10 cm

∴ Assertion (A) is false.

From the above calculation BC = 5 cm.

In Δ ACP, using Pythagoras Theorem,

AP2 = PC2 + AC2

⇒ 202 = 122 + AC2

⇒ 400 = 144 + AC2

⇒ AC2 = 400 - 144

⇒ AC2 = 256

⇒ AC = 256\sqrt{256}

⇒ AC = 16 cm

AB = AC - BC

= 16 cm - 5 cm

= 11 cm

∴ Reason (R) is true.

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

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