# Triangle A has sides of lengths #32 #, #40 #, and #16 #. Triangle B is similar to triangle A and has a side of length #8 #. What are the possible lengths of the other two sides of triangle B?

Three possible lengths of other two sides are

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

Since triangle B is similar to triangle A, the ratios of corresponding sides in the two triangles are equal. Let's denote the lengths of the corresponding sides of triangles A and B as follows:

( \frac{{\text{Side of Triangle B}}}{{\text{Side of Triangle A}}} = \frac{{8}}{{32}} = \frac{{\text{length of corresponding side in B}}}{{\text{length of corresponding side in A}}} )

( \frac{{\text{Side of Triangle B}}}{{\text{Side of Triangle A}}} = \frac{{8}}{{40}} = \frac{{\text{length of corresponding side in B}}}{{\text{length of corresponding side in A}}} )

( \frac{{\text{Side of Triangle B}}}{{\text{Side of Triangle A}}} = \frac{{8}}{{16}} = \frac{{\text{length of corresponding side in B}}}{{\text{length of corresponding side in A}}} )

Now, we can find the lengths of the other two sides of triangle B by multiplying the corresponding lengths of triangle A by the ratios calculated above.

For the first ratio ( \frac{{8}}{{32}} ), we find:

( \frac{{8}}{{32}} \times 40 = 10 )

For the second ratio ( \frac{{8}}{{40}} ), we find:

( \frac{{8}}{{40}} \times 32 = 6.4 )

For the third ratio ( \frac{{8}}{{16}} ), we find:

( \frac{{8}}{{16}} \times 40 = 20 )

So, the possible lengths of the other two sides of triangle B are 10, 6.4, and 20.

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.

- A triangle has corners at points A, B, and C. Side AB has a length of #32 #. The distance between the intersection of point A's angle bisector with side BC and point B is #12 #. If side AC has a length of #24 #, what is the length of side BC?
- Judy lies on the ground 45 feet from her tent. Both the top of the tent and the top of a tall cliff are in her line of sight. Her tent is 10 feet tall. About how high is the cliff? Assume the two triangles are similar?
- A triangle has corners at points A, B, and C. Side AB has a length of #15 #. 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 #9 #, what is the length of side BC?
- Triangle A has sides of lengths #15 #, #12 #, and #18 #. 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?
- Triangle A has an area of #24 # and two sides of lengths #8 # and #12 #. Triangle B is similar to triangle A and has a side of length #5 #. What are the maximum and minimum possible areas of triangle B?

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