Question

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!

Answer 1

The height is
`8.7\ cm`

Explanation:

step 1

Find the diagonal of the base

Applying the Pythagoras Theorem

`d^(2)=18^(2)+15^(2)\\ \\d^(2)=549\\ \\ d=√(549)\ cm`

step 2

Find the height of the prism

we know that

The diagonal of the rectangular prism is equal to

`D^(2)=d^(2)+h^(2)`

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

`d=√(549)\ cm`

`D=25\ cm`

substitute and solve for h

`25^(2)=(√(549))^(2)+h^(2)`

`h^(2)=625-549`

`h^(2)=76`

`h=8.7\ cm`