Question

GEOMETRY: PLEASE HELP!!

Answer 1

Answer:

$GF=72$

Step-by-step 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:

$GF=\frac{3}{2}EH, \\\\GF=\frac{3}{2}\cdot 48,\\\\GF=\boxed{72}$