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August 26th, 2019, 06:42 PM  #1 
Newbie Joined: May 2018 From: United States Posts: 8 Thanks: 0 Math Focus: Algebra  Algebra Pythagorean Theorem
Hello all. I was wondering how to solve this particular problem. I am not certain I am setting it up correctly, and I think it's likely I don't have it quite right. Any help is deeply appreciated. (from textbook) "Use the Pythagorean Theorem to find the missing side length. Leave answer in simplest form." $\displaystyle a= \frac{2}{3}b , c=12$ (my attempt) $\displaystyle \left (\frac{2}{3}b \right )^2+b^2=12^2$ Next I raise the contents of my first parenthesis to the second power, then combine like terms $\displaystyle b^2$. Thus $\displaystyle \frac{4}{9}b +b^2$ $\displaystyle \frac{13}{9}b^2 =144$ \Multiply both sides by reciprocal of b's coefficient $\displaystyle b^2=\frac{1296}{13}$ My guess at the solution is the same as above, just apply radical to right and remove b's 2nd power. I appreciate any and all input. My book provides no solution, so I don't know whether this is correct or miles off the mark. Last edited by skipjack; August 26th, 2019 at 10:59 PM. 
August 26th, 2019, 06:46 PM  #2 
Senior Member Joined: Sep 2015 From: USA Posts: 2,636 Thanks: 1472 
This is correct though as they are lengths, and thus nonnegative, you could go further and say that $b = \dfrac{36}{\sqrt{13}}=\dfrac{36\sqrt{13}}{13}$ 

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