Arectangular prism has a volumen of 96ft. the area of the bas is 24ft what is height of the prism?

The formula of a volume of a prism:

V = BH

B - area of a base

H - height

We have: V = 96ft³ and B = 24ft².

Substitute:

24H = 96 |:24

H = 4ft

The height of the prism is 4 ft.

we have three similar triangles, because each has a right angle and shares an angle.   let's write the angles in order: opposite to short leg, long leg, hypotenuse.

cab similar to bad similar to cbd

or as ratios,

ca: ab: cb = ba: ad: bd = cb: bd: cd

we also know

ac = ad + cd

(ad+cd): ab: cb = ba: ad: bd = cb: bd: cd

(ad+cd)/cb=cb/cd

we have cb=6, ad=5 and seek x=cd.

we reject the negative root and conclude x=4

answer: 4