# Thread: Rectangular Parallelepiped Length and Angle Problem Stuck:(!!

1. ## Rectangular Parallelepiped Length and Angle Problem Stuck:(!!

A rectanglar parallelepiped with square ends has 12 edges and six surfaces. If the sum of all edges is 176 cm and the total surface area is 1288 cm^(2)

Find:

A) the length of the diagonal of the parallelpiped (shown as bold line in figure)

B) the angle the diagonal makes with the base (two answers are possible)

Picture of figure is linked below

Thank You

2. ## Re: Rectangular Parallelepiped Length and Angle Problem Stuck:(!!

Originally Posted by ticaaal70
A rectanglar parallelepiped with square ends has 12 edges and six surfaces. If the sum of all edges is 176 cm and the total surface area is 1288 cm^(2)
So it has four sides of length x and eight sides (the square ends) of length y. "The sum of the edges is 176 cm"- so 4x+ 8y= 176. "The total surface area is 1288 cm^2"- so 2y^2+ 4xy= 1288. From 4x+ 8y= 176, 4x= 176- 8y, x=44- 2y. Then the area equation becomes 2y^2+ 4xy= 2y^2+ 4(44- 2y)y= 2y^2+ 176y- 8y^2= 176y- 6y^2= 1288. Solve 6y^2- 176y+ 1288= 0 for y, then find x. The diagonal in A can be found by two applications of the Pythagorean theorem. First find the length of that dashed line diagonal then use it as one leg of the second right triangle having the main diagonal as hypotenuse. Once you have that, you can use trigonometry on that right triangle to find the angle.

Find:

A) the length of the diagonal of the parallelpiped (shown as bold line in figure)

B) the angle the diagonal makes with the base (two answers are possible)

Picture of figure is linked below

Thank You