Question

Use the given figure to find the length of FG

Answer 1

The length of FG is
`19\:units`.

Explanation:

Since the altitude of the triangle bisects the third side, triangle FGH is isosceles.

Therefore
`|FG|=|HG|`

This implies that,

`5x-6=3x+4`

This is a linear equation where we easily solve for
`x`.

We group like terms to get,

`5x-3x=4+6`

`2x=10`

We divide both sides by 2 to obtain,

`x=5`.

The length of FG is

`5(5)-6=25-6=19`