Question

the edges of a tetrahedron measure 3,4,5,6,7 and 8 units. find the edges of a similar tetrahedron containing 27 times the volume. HEELLP ME PLLEEAASSEE!

Answer 1

If two solids are similar, the cube of the scale factor of the two solids is equal to the ratio of the volumes.

Let x be the length of the side of the larger, similar solid. Let be the side that corresponds to 3 in the smaller solid.

According to the theorem:

(1/x)^3 = (1/27)

(1/x)^3 = (1/3)^3

So, (1/x) = (1/3)

The scale factor from small to large is one to three.

So, triple the given edges of the smaller solid to get the lengths of the larger solid.

@sassy016