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# Difficult 3d - geometry prob!

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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  60. Find the length of the diagonal joining one corner of the prism to the opposite corner.

Apr 14, 2022

#1
+2455
+1

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 $$\color{brown}\boxed{13}$$

Apr 14, 2022

#1
+2455
+1

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 $$\color{brown}\boxed{13}$$

BuilderBoi Apr 14, 2022
#2
+124598
0

Very nice, BuilderBoi  !!!

{This one had me stumped....I loved the way you solved it !!!  }

CPhill  Apr 14, 2022
#3
+2455
0

Thanks! This isn't my solution... I used the same method used here: https://web2.0calc.com/questions/please-help_20818

BuilderBoi  Apr 14, 2022