Answer

Verified

430.2k+ views

**Hint:**Use a rough figure for the dimensions of the room. Calculate the length of the longest pole that can be accommodated in the room by calculating the length of the cuboid formed with dimensions of room. Use formula of diagonal of cuboid. Bring all possible values out of square root and write the final answer.

* A cuboid having dimensions l, b and h will have a length of diagonal as \[\sqrt {{l^2} + {b^2} + {h^2}} \].

**Complete answer:**

We are given that room has dimensions 5m \[ \times \]3m\[ \times \] 4m

Then we can write the length of room i.e. \[l = 5\]

We can write breadth of the room i.e. \[b = 3\]

We can write height of the room i.e. \[h = 4\]

Draw a figure for room having dimensions given above

Now we can see that if a pole is taken in any direction of the room it will be either of length 5m, 4, or 3m.

Since we know the diagonal of a cuboid has the largest length then we calculate the length of the diagonal of the cuboidal room.

\[ \Rightarrow \]Length of diagonal \[ = \sqrt {{l^2} + {b^2} + {h^2}} \]

Substitute the value of \[l = 5,b = 3,h = 4\]in the formula

\[ \Rightarrow \]Length of diagonal \[ = \sqrt {{5^2} + {3^2} + {4^2}} \]

Calculate the squares of terms under the square root

\[ \Rightarrow \]Length of diagonal \[ = \sqrt {25 + 9 + 16} \]

Calculate the sum under the square root

\[ \Rightarrow \]Length of diagonal \[ = \sqrt {50} \]

\[ \Rightarrow \]Length of diagonal \[ = \sqrt {25 \times 2} \]

We know \[25 = {5^2}\]

\[ \Rightarrow \]Length of diagonal \[ = \sqrt {{5^2} \times 2} \]

\[ \Rightarrow \]Length of diagonal \[ = 5\sqrt 2 \]

\[\therefore \]The length of the longest pole which can be accommodated in the hall is \[5\sqrt 2 \]m

**\[\therefore \]Option A is correct.**

**Note:**

Many students make the mistake of writing the value of length of longest pole as the longest dimension given in the question i.e. 5m which is wrong, keep in mind in a cuboidal figure the length of diagonal is the longest.

Recently Updated Pages

Who among the following was the religious guru of class 7 social science CBSE

what is the correct chronological order of the following class 10 social science CBSE

Which of the following was not the actual cause for class 10 social science CBSE

Which of the following statements is not correct A class 10 social science CBSE

Which of the following leaders was not present in the class 10 social science CBSE

Garampani Sanctuary is located at A Diphu Assam B Gangtok class 10 social science CBSE

Trending doubts

Derive an expression for drift velocity of free electrons class 12 physics CBSE

Which are the Top 10 Largest Countries of the World?

Write down 5 differences between Ntype and Ptype s class 11 physics CBSE

The energy of a charged conductor is given by the expression class 12 physics CBSE

Fill the blanks with the suitable prepositions 1 The class 9 english CBSE

Derive an expression for electric field intensity due class 12 physics CBSE

How do you graph the function fx 4x class 9 maths CBSE

The Equation xxx + 2 is Satisfied when x is Equal to Class 10 Maths

Derive an expression for electric potential at point class 12 physics CBSE