# A triangle has corners at points A, B, and C. Side AB has a length of #12 #. The distance between the intersection of point A's angle bisector with side BC and point B is #3 #. If side AC has a length of #9 #, what is the length of side BC?

Length of the side

By signing up, you agree to our Terms of Service and Privacy Policy

Using the angle bisector theorem, we can find the length of side BC.

Let D be the point where the angle bisector of angle A intersects side BC.

According to the angle bisector theorem:

[\frac{{BD}}{{DC}} = \frac{{AB}}{{AC}}]

Given that AB = 12 and AC = 9:

[\frac{{BD}}{{DC}} = \frac{{12}}{{9}} = \frac{4}{3}]

Let's denote the length of BD as x. Then DC = (3/4)x.

We're also given that the distance between D and B is 3.

So, x + (3/4)x = 3

Solving for x:

[x + \frac{3}{4}x = 3] [\frac{7}{4}x = 3] [x = \frac{3 \times 4}{7}] [x = \frac{12}{7}]

Now, the length of BC is BD + DC:

[BC = x + \frac{3}{4}x] [BC = \frac{12}{7} + \frac{3}{4} \times \frac{12}{7}] [BC = \frac{12}{7} + \frac{9}{7}] [BC = \frac{21}{7}] [BC = 3]

So, the length of side BC is 3.

By signing up, you agree to our Terms of Service and Privacy Policy

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

- Triangle A has sides of lengths #1 ,4 #, and #4 #. Triangle B is similar to triangle A and has a side of length #3 #. What are the possible lengths of the other two sides of triangle B?
- A triangle has corners at points A, B, and C. Side AB has a length of #7 #. The distance between the intersection of point A's angle bisector with side BC and point B is #6 #. If side AC has a length of #14 #, what is the length of side BC?
- A street sign casts a 12-foot 9-foot shadow. The lamppost next to it cast a 24-foot shadow. How tall is the lamppost?
- Triangle A has an area of #4 # and two sides of lengths #6 # and #4 #. Triangle B is similar to triangle A and has a side with a length of #9 #. What are the maximum and minimum possible areas of triangle B?
- As a man walks away from a 12 foot lamppost, the tip of his shadow moves twice as fast as he does. What is the man's height?

- 98% accuracy study help
- Covers math, physics, chemistry, biology, and more
- Step-by-step, in-depth guides
- Readily available 24/7