# Triangle A has an area of #12 # and two sides of lengths #4 # and #8 #. Triangle B is similar to triangle A and has a side of length #7 #. What are the maximum and minimum possible areas of triangle B?

##### 1 Answer

#### Explanation:

**First you must find the side lengths for the maximum sized triangle A** , when the longest side is greater than 4 and 8 **and the minimum sized triangle** , when 8 is the longest side.

To do this **use Heron's Area formula** :

Let

*Square both sides:*

*Pull out a 1/2 from each factor:*

*Simplify:*

*Substitute

*Use completing the square:*

*Square root both sides:*

Substitute

Since triangle side lengths are positive we need to ignore the negative answers:

**Minimum and maximum side lengths of triangle A:**

Since **the area of triangles are proportional to the square of the side lengths** we can find the maximum and minimum areas of triangle B: