# Triangle A has an area of #12 # and two sides of lengths #5 # and #7 #. Triangle B is similar to triangle A and has a side with a length of #19 #. What are the maximum and minimum possible areas of triangle B?

Maximum Area

Minimum Area

The triangles A and B are similar. By ratio and proportion method of solution, triangle B has three possible triangles.

For Triangle A: the sides are

The angle Z between sides x and y was obtained using the formula for area of triangle

Three possible triangles for Triangle B: the sides are

Maximum Area with Triangle 3. Minimum Area with Triangle 1.

God bless....I hope the explanation is useful.

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

To find the maximum and minimum possible areas of triangle B, we first need to determine the scale factor between triangles A and B, as they are similar triangles. Since one side of triangle B is 19 units long and corresponds to a side length of 7 units in triangle A, the scale factor between them is ( \frac{19}{7} ).

To find the maximum possible area of triangle B, we use the fact that the area of a similar triangle is proportional to the square of the scale factor. So, if the area of triangle A is 12 units(^2), then the maximum possible area of triangle B is ( 12 \times \left( \frac{19}{7} \right)^2 ).

To find the minimum possible area of triangle B, we again use the fact that the area of a similar triangle is proportional to the square of the scale factor. So, the minimum possible area of triangle B occurs when the scale factor is minimized. Since the side length of 19 in triangle B corresponds to a side length of 5 in triangle A, the scale factor is ( \frac{19}{5} ). Therefore, the minimum possible area of triangle B is ( 12 \times \left( \frac{19}{5} \right)^2 ).

Calculating these values, we find:

Maximum possible area of triangle B = ( 12 \times \left( \frac{19}{7} \right)^2 )

Minimum possible area of triangle B = ( 12 \times \left( \frac{19}{5} \right)^2 )

These values can be computed to obtain the numerical results for the maximum and minimum possible areas of triangle B.

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 #21 #. The distance between the intersection of point A's angle bisector with side BC and point B is #7 #. If side AC has a length of #28 #, what is the length of side BC?
- A triangle has corners at points A, B, and C. Side AB has a length of #35 #. The distance between the intersection of point A's angle bisector with side BC and point B is #14 #. If side AC has a length of #36 #, what is the length of side BC?
- Triangle A has sides of lengths #1 ,4 #, and #5 #. 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 #12 #. The distance between the intersection of point A's angle bisector with side BC and point B is #8 #. If side AC has a length of #19 #, what is the length of side BC?
- Triangle A has an area of #9 # and two sides of lengths #3 # and #8 #. Triangle B is similar to triangle A and has a side with a length of #7 #. 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