Triangle A has an area of $8$ $8$ and two sides of lengths $5$ $5$ and $9$ $9$ . Triangle B is similar to triangle A and has a side of length $12$ $12$ . What are the maximum and minimum possible areas of triangle B?

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Answer 1 · 2017-12-07T11:37:17

Maximum area 46.08 and Minimum area 14.2222

$Delta s A and B$ 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 $B =( 8 * 144) / 25= 46.08$

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 $Delta B = (8*144)/81= 14.2222$

Triangle A has an area of 8 88 and two sides of lengths 5 55 and 9 99 . Triangle B is similar to triangle A and has a side of length 12 1212 . What are the maximum and minimum possible areas of triangle B?