# Triangle A has an area of #18 # and two sides of lengths #8 # and #12 #. Triangle B is similar to triangle A and has a side with a length of #9 #. What are the maximum and minimum possible areas of triangle B?

##### 2 Answers

Maximum area of **729/32** & Minimum area of **81/8**

#### Explanation:

If sides are 9:12, areas will be in their square.

Area of B **81/8**

If the sides are 9:8,

Area of B **729/32**

Aliter :

For similar triangles, ratio of corresponding sides are equal.

Area of triangle A =18 and one base is 12.

Hence height of

If

Area of **81/8**

Area of

Hence height of

I

the height of

Area of **729/32**

**729/32** & Minimum area **81/8**

Minimum possible area **81/8**

Maximum possible area **729/32**

#### Explanation:

Alternate Method :

Sides ratio 9/12=3/4.Areas ratio will be

Sides ratio = 9/8.