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.
+2668 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?
+2668 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?
