Answer:
4.8 feet
Step-by-step explanation:
Since length and width of base is 3 and 2 respectively, we find the diagonal of the base with pythagorean theorem.
[tex]3^2+2^2=h^2\\9+4=h^2\\13=h^2\\h=\sqrt{13}[/tex]
This hypotenuse is the base of a triangle with height as the height of the prism and hypotenuse being the hypotenuse of the prism.
So we can again use pythagorean theorem to solve for the height of the prism (let height of prism be x)
[tex](\sqrt{13} )^2+x^2=6^2\\13+x^2=36\\x^2=36-13\\x^2=23\\x=\sqrt{23}[/tex]
To the nearest tenth, height is 4.8 feet
