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?

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.