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Mathematics

Assertion (A) : The length of the longest rod that can be put in a room of dimensions 10 m × 10 m × 5 m is 15 m.

Reason (R) : Length of the diagonal of a cuboid = l2+b2+h2\sqrt{l^2 + b^2 + h^2}

  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

Given,

Room dimensions = 10 m × 10 m × 5 m

The longest rod that can be placed in a room = Diagonal of room.

We know that,

Diagonal of cuboid = l2+b2+h2\sqrt{l^2 + b^2 + h^2}

Diagonal of room = 102+102+52\sqrt{10^2 + 10^2 + 5^2}

= 100+100+25\sqrt{100 + 100 + 25}

= 225\sqrt{225}

= 15 m.

So length of the longest rod that can be placed in the room = 15 m.

∴ Assertion (A) is true.

By formula,

Length of the diagonal of cuboid = l2+b2+h2\sqrt{l^2 + b^2 + h^2}

∴ Reason (R) is true.

Both Assertion (A) and Reason (R) are true.

Hence, option 3 is the correct option.

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