# Triangle A has an area of #3 # and two sides of lengths #3 # and #6 #. Triangle B is similar to triangle A and has a side with a length of #11 #. What are the maximum and minimum possible areas of triangle B?

##### 1 Answer

Feb 17, 2016

The **triangle inequality** states that the sum of any two sides of a triangle MUST be greater than the 3rd side. That implies the missing side of triangle A must be **greater than 3!**

#### Explanation:

Using the triangle inequality ...

So, the missing side of triangle A must fall between 3 and 6.

This means **3** is the **shortest** side and **6** is the **longest** side of triangle A.

Since **area is proportional to the square of the ratio of the similar sides** ...

**minimum area**

**maximum area**

Hope that helped

P.S. - If you really want to know the length of the missing 3rd side of triangle A, you can use **Heron's area formula** and determine that the length is