Symmetry

AD, EF and BD are perpendicular to AB.

AD = 3 and BC = 5

What is the length h?

Quote:

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?

Quote:

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