The volume of a cube is V=s3 , where s is the length of one edge of the cube. What is the edge length s for each cube?

look at the picture for the answer choices:)

s =

Step-by-step explanation:

V = s^3

Plug in the given volume.

999 = s^3

Take the third root of both sides to cancel out the ^3.

= s

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