Question

Use the given figure to find the length of FG

Answer 1

The length of side FG is 19 units.

Explanation:

Let the midpoint of FH be P.

In triangle FGP and triangle HGP,

`FP=HP` (Given)

`\angle FPG=\angle HPG=90^(\circ)` (Given)

`PG=PG` (Common side)

By SAS postulate,

`\triangle FGP\cong \triangle HGP`

Now,

`FG=HG` (CPCTC)

`5x-6=3x+4`

`2x=10`

`x=5`

The value of x is 5.

`FG=5(5)-6=19`

Therefore the length of side FG is 19 units.