# Triangle A has an area of 60  and two sides of lengths 12  and 15 . Triangle B is similar to triangle A and has a side of length 5 . What are the maximum and minimum possible areas of triangle B?

Dec 7, 2017

Maximum area 10.4167 and Minimum area 6.6667

#### Explanation:

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

To get the maximum area of $\Delta B$, side 5 of $\Delta B$ should correspond to side 12 of $\Delta A$.

Sides are in the ratio 5 : 12
Hence the areas will be in the ratio of ${5}^{2} : {12}^{2} = 25 : 144$

Maximum Area of triangle $B = \frac{60 \cdot 25}{144} = 10.4167$

Similarly to get the minimum area, side 15 of $\Delta A$ will correspond to side 5 of $\Delta B$.
Sides are in the ratio $5 : 15$ and areas $25 : 225$

Minimum area of $\Delta B = \frac{60 \cdot 25}{225} = 6.6667$