Is the perimeter numerically equal to the area in this equation?

  • MHB
  • Thread starter mathdad
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In summary, the question is asking to show that (1/2)uv is equal to u + v + w, based on the given equations for u, v, and w. The best approach is to start with the final equation and work backwards, ensuring that each step is reversible. This will prove the desired result.
  • #1
mathdad
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If u = 2(m + n)/n, and v = 4m/(m - n), and

w = 2(m^2 + n^2)/(m - n)n, show that

(1/2)uv = u + v + w (that is, the perimeter is numerically equal to the area).

This question is basically a plug and chug situation.
I must multiply (1/2) by the given values of u and v on the left side. I must then replace u, v and w on the right side with their given values and add. The right side must = the left side, right?
 
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  • #2
Yes, it looks like the simplest way to do this is NOT "directly", starting from the given values of u, v, and w and then showing the final equation, but "indirectly", starting from the final equation then working to the equations for u, v, and w. As long as every step is "reversible", that will prove what you want.
 
  • #3
I will work this out when time allows. Interesting question.
 

FAQ: Is the perimeter numerically equal to the area in this equation?

What does the equation (1/2)uv = u + v + w mean?

The equation (1/2)uv = u + v + w is a mathematical expression that represents the relationship between three variables, u, v, and w. The left side of the equation indicates that half of the product of u and v is equal to the sum of u, v, and w on the right side.

How is this equation used in science?

This equation is commonly used in science to represent various relationships between quantities. For example, it can be used to calculate the average of two quantities, or to express the concept of conservation of energy.

What do the variables u, v, and w represent in this equation?

The variables u, v, and w can represent any quantities or values that are related to each other. They can represent physical quantities such as distance, time, or energy, or they can represent abstract concepts such as variables in a mathematical equation.

Can this equation be rearranged to solve for a specific variable?

Yes, this equation can be rearranged to solve for a specific variable if the values of the other two variables are known. For example, if the values of u and v are known, the equation can be rearranged to solve for w.

Are there any limitations to using this equation?

Like any mathematical equation, there may be certain limitations to using this equation depending on the context in which it is being applied. For example, it may not be applicable to certain systems or situations that do not follow the assumptions of the equation.

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