# Optimizing Kite Area: Solving x,y,z for Max Area

• trajan22
In summary, the conversation discusses finding the maximum area of a kite using the equation (x*y)+(z*x)=A, with A and B being fixed constants. The approach suggested is to solve for y and z in terms of x, then differentiate and set it equal to zero. Two additional equations are needed to relate A to x and y, and B to x and z.
trajan22
I have a kite pictured below...i need to determine x y z so that the kite has a maximum area. a and b are fixed constants.

The way I am thinking of trying this is to have this equation
(x*y)+(z*x)=A
from this i have three variables so i should solve for y in terms of x and solve for z in terms of x this will give me one equation one unknown so i can differentiate and set it equal to zero. therefore solving.

Would this be a correct approach for this problem...(sorry about the poor drawing, its difficult on a touchpad)

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I think you mean xy + zx = area

A and B are fixed constants. You need to make two more equations relating A to x and y, and B to x and z.

so for those other 2 eqs would it be A^2=x^2+Y^2
B^2=x^2+z^2

## What is the purpose of optimizing kite area?

The purpose of optimizing kite area is to find the maximum area that a kite can cover using a given amount of material. This allows for the creation of more efficient and effective kites.

## What factors affect the area of a kite?

The area of a kite is affected by the length and width of the kite, as well as the angle at which the kite is flown. Other factors such as wind speed and air pressure can also impact the area of a kite.

## How do you solve for x, y, and z in optimizing kite area?

Solving for x, y, and z in optimizing kite area involves using mathematical equations and principles, such as geometry and calculus, to find the optimal values for these variables. This process may also involve trial and error and making adjustments to the design of the kite.

## What are some real-world applications of optimizing kite area?

Optimizing kite area has various real-world applications, such as in the design of wind turbines and aircraft wings. It can also be used in the development of more efficient parachutes and other aerial devices.

## What are the benefits of optimizing kite area?

The benefits of optimizing kite area include creating more efficient and effective kites, reducing material and production costs, and improving overall performance and functionality. It can also lead to advancements in other fields, such as renewable energy and transportation.

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