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!

Question

asked Aug 21, 2020 109k views

1 Answer

Uyric · Answer 1 · 2020-08-26T16:02:58+0000

Answer:

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

$h=8.7\ cm$