Question

BD is the altitude to the hypotenuse AC.
http://secure.starssuite.com/files/geo2010/Geom_10S_Fig24.jpg

What is the length of BD?

What is the length of AD?

Answer 1

Have you heard of the right triangle altitude theorem?

Answer 2

no:o

Answer 3

It is made up of two parts.
I'll write the two parts.
Then I'll tell you which one you need to use.

Answer 4

okay

Answer 5

Right Triangle Altitude Theorem

Part 1: The length of the altitude drawn from the vertex of the right angle of a right triangle to its hypotenuse is the geometric mean between the lengths of the two segments of the hypotenuse.

Part 2: If the altitude is drawn to the hypotenuse of a right triangle, then the length of each leg of the right triangle is the geometric mean of the lengths of hypotenuse and the segment of the hypotenuse adjacent to the leg.

Answer 6

The segments in your figure of lengths 3 and 12, AB and BC, are the segments of the hypotenuse.

Answer 7

You need to know how to calculate a geometric mean.
The geometric mean of numbers a and b is \(\sqrt{ab} \) .

Answer 8

The first question is length BD.
BD is the altitude of the large right triangle.

Answer 9

To find BD we need Part 1 of the theorem.

Part 1: The length of the altitude drawn from the vertex of the right angle of a right triangle to its hypotenuse is the geometric mean between the lengths of the two segments of the hypotenuse.

Answer 10

The length of BD is the geometric mean between 3 and 12.
All you need to do is find the geometric mean of 3 and 12.

That is: \(\sqrt{3 \times 12} \)

Answer 11

thank you!!

Answer 12

That takes care of the first question.
Then you have the second question.
Use part 2 of the theorem for the second question.

Answer 13

You're welcome.