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Consider the following diagram:

Then what are the lengths of AE and CE equal to, in that order?

 Jul 11, 2022
 #1
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AE = 5*sqrt(2), CE = 3*sqrt(3)

 Jul 11, 2022
 #2
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Let \(AE= x \) and \(CE = y\)

 

From \(\triangle AEC\), we have the equation: \(x^2 + y^2 = 81\)

 

Using the Pythagorean Theorem on \(\triangle CAD\) and \(\triangle DAB\), we find that \(DB = 12 \sqrt {2} \)

 

Also, from \(\triangle BEC\), we have the equation: \((x+7)^2 + y^2 = (12 \sqrt 2)^2\)

 

Now we just need to solve the system for x and y. 

 

Can you take it from here?

 Jul 12, 2022

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