# Triangle A has an area of 7  and two sides of lengths 4  and 9 . Triangle B is similar to triangle A and has a side with a length of 7 . What are the maximum and minimum possible areas of triangle B?

Dec 7, 2017

Maximum area 21.4375 and Minimum area 4.2346

#### Explanation:

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

To get the maximum area of $\Delta B$, side 7 of $\Delta B$ should correspond to side 4 of $\Delta A$.

Sides are in the ratio 7 : 4
Hence the areas will be in the ratio of ${7}^{2} : {4}^{2} = 49 : 16$

Maximum Area of triangle B =( 7 * 49 / 16= 21.4375

Similarly to get the minimum area, side 9 of $\Delta A$ will correspond to side 7 of $\Delta B$.
Sides are in the ratio $7 : 9$ and areas $49 : 81$

Minimum area of $\Delta B = \frac{7 \cdot 49}{81} = 4.2346$