Concept explainers
To calculate: To compare the rate of change of perimeter of regular hexagon with the rate of change for a perimeter of square.
Answer to Problem 4GP
The rate of change of perimeter of hexagon
Explanation of Solution
Given information: The side of a regular hexagon increases by
Formula Used:
Perimeter is defined as the sum of all the sides of the figure.
Perimeter of square
Perimeter of hexagon
Calculation:
Let the length of the side of hexagon be
Now, perimeter of regular hexagon
Perimeter of square
Given that the side of a regular hexagon increases by
Thus,
New Perimeter of regular hexagon
New Perimeter of square
Now,
Rate of change of perimeter of regular hexagon is calculated as
Also, rate of change of perimeter of square is calculated as
On comparing the rate of change of perimeter of hexagon with rate of change of perimeter of square,
Conclusion:
Hence, the rate of change of perimeter of hexagon
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