# Triangle A has an area of 5  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 20, 2017

Maximum area of triangle B = 45

Minimum area of triangle B = 11.25

#### Explanation:

Triangle A sides 6,3 & area 5.

Triangle B side 9

For maximum area of triangle B : side 9 will be proportional to side 3 of triangle A.
Then the side ratio is 9:3. Therefore, areas will be in the ratio of
${9}^{2} : {3}^{3} = \frac{81}{9} = 9$
$\therefore$ Maximum Area of triangle $B = 5 \cdot 9 = 45$

Similarly, for minimum area of triangle B,
side 9 of triangle B will correspond to side 6 of triangle A.
Sides ratio $= 9 : 6$and areas ratio $= {9}^{2} : {6}^{2} = 9 : 4 = 2.25$
$\therefore$ Minimum area of triangle $B = 5 \cdot 2.25 = 11.25$