# Math Help - Symmetry

1. ## Symmetry

AD, EF and BD are perpendicular to AB.

AD = 3 and BC = 5

What is the length h?

2. Originally Posted by Natasha1
AD, EF and BD are perpendicular to AB.

AD = 3 and BC = 5

What is the length h?
You mean probably that AD,EF and BC are perpendicular to AB?

3. Originally Posted by Natasha1
AD, EF and BD are perpendicular to AB.

AD = 3 and BC = 5

What is the length h?
As triangles ABD and DBF are similar:

$
\frac{h}{3}=\frac{DB}{AB}\ \ \ \dots (1)
$

Also trianglea ABC and ADF are similar:

$
\frac{h}{5}=\frac{AB-DB}{AB}
$

So dividing these:

$
\frac{5}{3}=\frac{DB}{AB}\ \frac{AB}{AB-DB}=\frac{DB}{AB-DB}
$

Hence:

$
DB=\frac{5}{8}AB
$

Substituting this into $(1)$ then gives:

$
\frac{h}{3}=\frac{5}{8}
$
,

or:

$
h=\frac{3\times 5}{8}=\frac{15}{8}
$

RonL