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# Find the length of the largest pole that can be placed in a room of dimensions 12 m × 4 m × 3 m.

**Solution:**

The Length of the largest pole that can be placed in a room is the length of the diagonal between the two extreme corners of the room as shown below:

So we have to calculate the length of AC. That will be the length of the longest pole that can be kept in the room.

To calculate AC we have to calculate the length of AB. Now △ABD is a __right angled triangle__ with:

AD = 12m

BD = 4m

Therefore,

AB² = BD² + AD²

AB² = (4)² + (12)²

AB² = 16 + 144

AB² = 160

Now to calculate AC we consider the △ACB which is also a right angled triangle. Therefore,

AC² = AB² + BC²

AC² = 160 + (3)²

AC² = 160 + 9

AC² = 169

AC = √169

AC = 13 m

Therefore the longest pole that can be kept in the room is 13 m

**✦ Try This: **Find the length of the largest pole that can be placed in a room of dimensions 10 m × 5 m × 4 m.

The Length of the largest pole that can be placed in a room is the length of the diagonal between the two extreme corners of the room as shown below:

So we have to calculate the length of AC. That will be the length of the longest pole that can be kept in the room.

To calculate AC we have to calculate the length of AB. Now △ABD is a right angled triangle with:

AD = 10m

BD = 5 m

Therefore,

AB² = BD² + AD²

AB² = (5)² + (10)²

AB² = 25 + 100

AB² = 125

Now to calculate AC we consider the △ACB which is also a right angled triangle. Therefore,

AC² = AB² + BC²

AC² = 125 + (4)²

AC² = 125 + 16

AC² = √141

AC = 11.87m

Therefore the longest pole that can be kept in the room is 11.87m.

**☛ Also Check: **NCERT Solutions for Class 8 Maths Chapter 11

**NCERT Exemplar Class 8 Maths Chapter 11 Problem 75**

## Find the length of the largest pole that can be placed in a room of dimensions 12 m × 4 m × 3 m.

**Summary:**

The length of the largest pole that can be placed in a room of dimensions 12 m × 4 m × 3 m is 13m

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