# Triangle A has an area of 6  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?

Dec 7, 2017

Maximum area 7.5938 and Minimum area 3.375

#### Explanation:

$\Delta s A \mathmr{and} B$ are similar.

To get the maximum area of $\Delta B$, side 9 of $\Delta B$ should correspond to side 8 of $\Delta A$.

Sides are in the ratio 9 : 8
Hence the areas will be in the ratio of ${9}^{2} : {8}^{2} = 81 : 64$

Maximum Area of triangle $B = \frac{6 \cdot 81}{64} = 7.5938$

Similarly to get the minimum area, side 12 of $\Delta A$ will correspond to side 9 of $\Delta B$.
Sides are in the ratio $9 : 12$ and areas $81 : 144$

Minimum area of $\Delta B = \frac{6 \cdot 81}{144} = 3.375$