Question

GEOMETRY: PLEASE HELP!!

Answer 1

`GF=72`

Explanation:

All triangles in the given figure are similar, from SAS. Notice that marked in the diagram,
`CD=DE=EF=FA`.

For triangle
`\triangle CGF` was base
`GF`, leg
`CF` contains three of these marked segments. In triangle
`\triangle CHE` with base
`HE`, leg
`CE` has two of these marked segments. By definition, similar polygons have corresponding sides in a constant proportion. Therefore, the length of GF must be
`3/2` the length of EH. Since the length of EH is given as 48, we have:

`GF=(3)/(2)EH, \\\\GF=(3)/(2)\cdot 48,\\\\GF=\boxed{72}`