# Triangle A has an area of 4  and two sides of lengths 6  and 3 . 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?

Oct 16, 2017

Largest possible area 36
Smallest possible area 16

#### Explanation:

Maximum possible are when side with length 9 in triangle B is the side similar to length 3 in Triangle A.
Area of triangles will be proportional in square of sides.

$\therefore$ Area of triangle #B = (9/3)^2*4=36

For minimum possible area, side with length 9 is proportional to side with length 6 in triangle A.

$\therefore$ Area of triangle $B = {\left(\frac{6}{3}\right)}^{2} \cdot 4 = 16$.