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# Triangle A has an area of 18  and two sides of lengths 5  and 9 . Triangle B is similar to triangle A and has a side of length 12 . What are the maximum and minimum possible areas of triangle B?

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Oct 24, 2017

Maximum area of triangle B = 103.68

Minimum area of triangle B = 32

#### Explanation:

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

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

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

Maximum Area of triangle $B = \frac{18 \cdot 144}{25} = 103.68$

Similarly to get the minimum area, side 9 of $\Delta A$ will correspond to side 12 of $\Delta B$.
Sides are in the ratio $12 : 9$ and areas $144 : 81$

Minimum area of $\Delta B = \frac{18 \cdot 144}{81} = 32$

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