# Triangle A has an area of 4  and two sides of lengths 8  and 3 . Triangle B is similar to triangle A and has a side with a length of 8 . What are the maximum and minimum possible areas of triangle B?

Oct 13, 2017

Minimum possible area o B 4
Maximum possible area of B 28(4/9) or 28.44

#### Explanation:

Since the triangles are similar, sides are in same proportion.

Case (1) Minimum possible area
$\frac{8}{8} = \frac{a}{3} \mathmr{and} a = 3$ Sides are 1:1
Areas will be square of the sides ratio $= {1}^{2} = 1$
$\therefore A r e a \Delta B = 4$

Case (2) Maximum possible area
$\frac{8}{3} = \frac{a}{8} \mathmr{and} a = \frac{64}{3}$ Sides are 8:3
Areas will be ${\left(\frac{8}{3}\right)}^{2} = \frac{64}{9}$
$\therefore A r e a \Delta B = \left(\frac{64}{9}\right) \cdot 4 = \frac{256}{9} = 28 \left(\frac{4}{9}\right)$