1. ## Rectangular Prism

A right rectangular prism has the following dimensions, x, y, z, where x + y + z = 15. Suppose that the prism's main diagonal has a length of 11. Then, determine the total surface area of the prism.

2. Originally Posted by Ideasman
A right rectangular prism has the following dimensions, x, y, z, where x + y + z = 15. Suppose that the prism's main diagonal has a length of 11. Then, determine the total surface area of the prism.
So,
$x+y+z=15$
Square,
$(x+y+z)^2 = 15^2 = 225$
Open,
$x^2+y^2+z^2+2xy+2xz+2yz = 225$
But,
$\sqrt{x^2+y^z+z^2}=11$
Thus,
$121 + 2xy+2xz+2yz = 225$
Thus,
$2xy+2xz+2yz = 104$