Two pyramids are similar. The volume of the larger pyramid is 125 mº and the volume of the smaller pyramid is 27 mº. The height of the smaller pyramid is 3 m What is the height of the larger pyramid? Enter your answer in the box.​

5 m

Step-by-step explanation:

= 5

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