Area of hexagon is maximum while perimeter is fixed

I'll make sure to do so in the future.In summary, the problem is to express the unknown variable y in terms of x, with a fixed perimeter P. The proposed solution is to represent y in terms of P and x, allowing the area A to be expressed in terms of just x. The person thanks for the help and apologizes for not reading the posting guidelines beforehand.
  • #1
nmr
7
0
this is the given problem:

ImageUploadedByPhysics Forums1410578071.067986.jpg


and this is my attempt at a solution:

ImageUploadedByPhysics Forums1410578438.619871.jpg


I am stuck here as the variable y is unknown and I want to express y in terms of x, but cannot figure out how to do so.
Thanks for any help!
 
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  • #2
nmr said:
this is the given problem:

View attachment 73096

and this is my attempt at a solution:

View attachment 73097

I am stuck here as the variable y is unknown and I want to express y in terms of x, but cannot figure out how to do so.
Thanks for any help!

Do not post thumbnails. Please read the 'pinned' thread 'Guidelines for students and helpers', which explains the reasons for this policy.
 
  • #3
You're told that the perimeter is fixed, which means that P is some constant. You can represent y in terms of P and x so that you then have the area A in terms of just one variable x.
 
  • #4
I got it, thanks alot!

Also sorry for not reading the posting guidelines beforehand.
 

Related to Area of hexagon is maximum while perimeter is fixed

1. What is the maximum area of a hexagon with a fixed perimeter?

The maximum area of a hexagon with a fixed perimeter is achieved when the hexagon is regular, meaning all sides are equal in length and all angles are equal. In this case, the maximum area is approximately 2.598 times the square of the length of one side.

2. How do you calculate the area of a hexagon with a fixed perimeter?

To calculate the area of a hexagon with a fixed perimeter, divide the perimeter by 6 to find the length of each side. Then, use the formula A = (3√3/2) * s^2, where A is the area and s is the length of one side. This formula applies to regular hexagons with equal sides.

3. Why is the area of a hexagon maximum when the perimeter is fixed?

This is because a regular hexagon has the most symmetrical shape with a fixed perimeter. Other shapes, such as irregular hexagons, may have the same perimeter but less area because the sides are not equal in length.

4. Can a hexagon have an infinite area with a fixed perimeter?

No, it is not possible for a hexagon to have an infinite area with a fixed perimeter. As the number of sides increases, the hexagon will approach a circle, which has the maximum area for a given perimeter. A circle cannot have an infinite area, therefore a hexagon cannot either.

5. Does the maximum area of a hexagon with a fixed perimeter vary depending on the units used for measurement?

No, the maximum area of a hexagon with a fixed perimeter is independent of the units used for measurement. As long as the length of the sides and perimeter are measured using the same units, the maximum area will remain constant. However, the numerical value of the area may vary depending on the units used.

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