**Ques: What is the length of the longest pole that can be placed in a room 24 m long, 16 m wide and 18 m high?**

A) 24 m

B) 28 m

C) 34 m

D) 42 m

**Ans. C) 34 m**

**Explanation:**

**The longest pole that can be placed in a room 24 m long, 16 m wide and 18 m high is AD as shown below in diagram**

**To find AD first we need to find AC**

As we know that every angle inside a cuboid is 90° also if a triangle has right angle we can use Pythagoras Theorem in it to find the sides i.e., Base, Perpendicular and Hypotenuse

**In triangle ABC using PGT (Pythagoras Theorem)**

**AC² = AB² + BC²**

**AC² = 24² + 16²**

**AC² = 576 + 256**

**AC² = 832**

**AC = √832**

**Now in triangle ACD using PGT**

**AD² = AC² + CD²**

**AD² = (√832)² + (18)²**

**AD² = 832 + 324**

**AD² = 1156**

**AD = √1156 = √34×34**

**AD = 34m**

__Ans__

**Thus the length of longest pole that can be placed in a room 24 m long, 16 m wide and 18 m high is 34 m.**

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