# Triangle A has an area of 25  and two sides of lengths 9  and 6 . Triangle B is similar to triangle A and has a side of length 8 . What are the maximum and minimum possible areas of triangle B?

Jun 11, 2016

Area ob B could be 19.75 or 44.44

#### Explanation:

The areas of similar figures are in the same ratio as the ratio of the squares of the sides.
In this case we do not know whether triangle b is bigger or smaller than triangle A, so we will have to consider both possibilities.

If A is bigger:$\text{ " 9^2/8^2 = 25/x " } \Rightarrow x = \frac{{8}^{2} \times 25}{9} ^ 2$

Area = $19.75$

If A is smaller:$\text{ " 6^2/8^2 = 25/x " } \Rightarrow x = \frac{{8}^{2} \times 25}{6} ^ 2$

Area = $44.44$