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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