A rectangular prism has a total surface area of 56 Also, the sum of all the edges of the prism is 60. Find the length of the diagonal joining one corner of the prism to the opposite corner.
+2668 The length of the diagonal can be derived from the formula: \(\sqrt {x^2 +y^2 + z^2}\).
From the given information, we can form two equations: \(4x+4y+4z=60\) and \(2xy+2yz+2zx=56\)
Simplifying the first equation, we have: \(x+y+z=15\).
Squaring the first equation, we get: \(x^2+y^2+z^2+2xy+2xz+2zy=225\)
SUbsituting what we know, we have: \(x^2+y^2+z^2 = 169\)
Now, we can take the sqaure root of this eqaution, to find that the diagonal has length \(\color{brown}\boxed{13}\)
+2668 The length of the diagonal can be derived from the formula: \(\sqrt {x^2 +y^2 + z^2}\).
From the given information, we can form two equations: \(4x+4y+4z=60\) and \(2xy+2yz+2zx=56\)
Simplifying the first equation, we have: \(x+y+z=15\).
Squaring the first equation, we get: \(x^2+y^2+z^2+2xy+2xz+2zy=225\)
SUbsituting what we know, we have: \(x^2+y^2+z^2 = 169\)
Now, we can take the sqaure root of this eqaution, to find that the diagonal has length \(\color{brown}\boxed{13}\)
+130071 Very nice, BuilderBoi !!!
{This one had me stumped....I loved the way you solved it !!! }
+2668 Thanks! This isn't my solution... I used the same method used here: https://web2.0calc.com/questions/please-help_20818
