# Triangle A has an area of #12 # and two sides of lengths #6 # and #9 #. Triangle B is similar to triangle A and has a side of length #15 #. What are the maximum and minimum possible areas of triangle B?

##### 2 Answers

Maximum area of

Minimum area of

#### Explanation:

Similar triangles have identical angles and size ratios. That means the **change** in length of any side either larger or smaller will be the same for the other two sides. As a result, the area of the

**It has been shown that if the ratio of the sides of similar triangles is R, then the ratio of the areas of the triangles is #R^2#.**

Example: For a

But if all three sides are **doubled** in length, the area of the new triangle is

From the information given, we need to find the areas of two new triangles whose sides are increased from either

Here we have

We also have **larger**

The ratio of the change in area of

The ratio of the change in area of

The minimum is

#### Explanation:

THIS ANSWER MAY BE INVALID AND IS AWAITING RECALCULATION AND DOUBLE CHECK! Check EET-APs answer for a tried-and-true method of solving the problem.

Because the two triangles are similar, call them triangle

Start by recalling Heron's theorem

We can now use this information to find the areas. If