Answer:
The height is [tex]8.7\ cm[/tex]
Step-by-step explanation:
step 1
Find the diagonal of the base
Applying the Pythagoras Theorem
[tex]d^{2}=18^{2}+15^{2}\\ \\d^{2}=549\\ \\ d=\sqrt{549}\ cm[/tex]
step 2
Find the height of the prism
we know that
The diagonal of the rectangular prism is equal to
[tex]D^{2}=d^{2}+h^{2}[/tex]
where
D is the diagonal of the rectangular prism
h is the height of the prism
d is the diagonal of the base of the rectangular prism
we have
[tex]d=\sqrt{549}\ cm[/tex]
[tex]D=25\ cm[/tex]
substitute and solve for h
[tex]25^{2}=(\sqrt{549})^{2}+h^{2}[/tex]
[tex]h^{2}=625-549[/tex]
[tex]h^{2}=76[/tex]
[tex]h=8.7\ cm[/tex]
