# The DeltasABC and FGH shown below are similar. Find bar(FH)?

##### 1 Answer
Mar 14, 2017

$\overline{F H} = 20$

#### Explanation:

As the corresponding angles in $\Delta A B C$ are congruent to the corresponding angles in $\Delta F G H$, we have

$\frac{A B}{F G} = \frac{B C}{G H} = \frac{A C}{F H}$

Now as $A B = 6$, $A C = 8$, $F G = x + 10$ and $F H = 4 x$, we have

$\frac{6}{x + 10} = \frac{8}{4 x}$

i.e. $6 \times 4 x = 8 \left(x + 10\right)$

or $24 x = 8 x + 80$

or $16 x = 80$

i.e. $x = \frac{80}{16} = 5$

and hence $\overline{F H} = 4 \times 5 = 20$