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A rectangular prism has a total surface area of 56. Also, the sum of all the edges of the prism is \(62\). Find the length of the diagonal joining one corner of the prism to the opposite corner.

 Apr 20, 2022

Best Answer 

 #1
avatar+2455 
+1

We have: \(4x+4y+4z=62\) and \(2xy+2yz+2xz=56\)

 

Simplifying the first equation, we get: \(x+y+z=15.5\)

 

Recall that \((x+y+z)^2=x^2+y^2+z^2+2xy+2yz+2xz\)

 

Substituting what we know, we have: \(x^2+y^2+z^2+56=240.25\)

 

We can transform this equation to: \(x^2+y^2+z^2=184.25\)

 

The length of the diagonal is: \(\sqrt{x^2+y^2+z^2}\)

 

Can you find the answer now?

 Apr 20, 2022
 #1
avatar+2455 
+1
Best Answer

We have: \(4x+4y+4z=62\) and \(2xy+2yz+2xz=56\)

 

Simplifying the first equation, we get: \(x+y+z=15.5\)

 

Recall that \((x+y+z)^2=x^2+y^2+z^2+2xy+2yz+2xz\)

 

Substituting what we know, we have: \(x^2+y^2+z^2+56=240.25\)

 

We can transform this equation to: \(x^2+y^2+z^2=184.25\)

 

The length of the diagonal is: \(\sqrt{x^2+y^2+z^2}\)

 

Can you find the answer now?

BuilderBoi Apr 20, 2022

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