A rectangular prism has a base of 18 cm by 15 cm and a diagonal of 25 cm. Identify its height. Round to the nearest tenth. HELP PLEASE!
Accepted Solution
A:
Answer:The height is [tex]8.7\ cm[/tex]Step-by-step explanation:step 1Find the diagonal of the baseApplying the Pythagoras Theorem[tex]d^{2}=18^{2}+15^{2}\\ \\d^{2}=549\\ \\ d=\sqrt{549}\ cm[/tex]step 2Find the height of the prismwe know thatThe diagonal of the rectangular prism is equal to[tex]D^{2}=d^{2}+h^{2}[/tex]whereD is the diagonal of the rectangular prismh is the height of the prismd is the diagonal of the base of the rectangular prismwe 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]