Calculate the total area of this rectangle

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To calculate the total area of a rectangle, the equations x + y = 15, 15 * 2y = A, and 15 * 3x = A can be used, where A represents the area. Substituting values, such as x = 6 and y = 9, can help verify the calculations. It is noted that there is a spelling error with the word "height." The discussion emphasizes the importance of setting up a proper system of equations to find the area. Understanding these relationships is crucial for accurate area calculations.
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Homework Statement
I was just wondering if someone could take a look at my solution. Not sure if it is correct. Im supposed to calculate the total area of the rectangle.
Relevant Equations
A= base* hight
1585595548878.png
 
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You can check that you are right by trying ##x=6, y=9## to see whether it all adds up!
 
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The only error I can find is that you have misspelled "height"!
 
Without looking at the responses which came after #1 posting,

You can identify three equations for a system:
x+y=15
15*2y=A
15*3x=A
A is for Area and x and y are as you assigned in your picture.
The system should indicate what steps can follow.
 
I tried to combine those 2 formulas but it didn't work. I tried using another case where there are 2 red balls and 2 blue balls only so when combining the formula I got ##\frac{(4-1)!}{2!2!}=\frac{3}{2}## which does not make sense. Is there any formula to calculate cyclic permutation of identical objects or I have to do it by listing all the possibilities? Thanks
Since ##px^9+q## is the factor, then ##x^9=\frac{-q}{p}## will be one of the roots. Let ##f(x)=27x^{18}+bx^9+70##, then: $$27\left(\frac{-q}{p}\right)^2+b\left(\frac{-q}{p}\right)+70=0$$ $$b=27 \frac{q}{p}+70 \frac{p}{q}$$ $$b=\frac{27q^2+70p^2}{pq}$$ From this expression, it looks like there is no greatest value of ##b## because increasing the value of ##p## and ##q## will also increase the value of ##b##. How to find the greatest value of ##b##? Thanks
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