Question

the height of a rectangular prism with a 6 in. by 10 in. base and a 13 in diagonal

Answer 1

The formula to find the diagonal of a rectangular prism is \[a^2+b^2+c^2=d^2\]
a, b, c represent the dimensions of the prism, while d is the diagonal. If you substitute in the given values, then you will be able to find the height.
a=?, b=6, c=10, d=13
\[a^2+6^2+10^2=13^2\]\[a^2+136=169\]\[a^2=33\]\[a=\sqrt{33}\]
The height of the rectangular prism is √33.