# Triangle A has an area of 27  and two sides of lengths 12  and 15 . Triangle B is similar to triangle A and has a side with a length of 25 . What are the maximum and minimum possible areas of triangle B?

Oct 24, 2017

Maximum area of triangle B = 108.5069

Minimum area of triangle B = 69.4444

#### Explanation:

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

To get the maximum area of $\Delta B$, side 25 of $\Delta B$ should correspond to side 12 of $\Delta A$.

Sides are in the ratio 25 : 12
Hence the areas will be in the ratio of ${25}^{2} : {12}^{2} = 625 : 144$

Maximum Area of triangle $B = \frac{25 \cdot 625}{144} = 108.5069$

Similarly to get the minimum area, side 15 of $\Delta A$ will correspond to side 25 of $\Delta B$.
Sides are in the ratio $25 : 15$ and areas $625 : 225$

Minimum area of $\Delta B = \frac{25 \cdot 625}{225} = 69.4444$