Triangle A has an area of $18$ $18$ and two sides of lengths $8$ $8$ and $7$ $7$ . Triangle B is similar to triangle A and has a side of length $5$ $5$ . What are the maximum and minimum possible areas of triangle B?

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Answer 1 · 2017-12-21T12:18:58

Maximum possible area of triangle B = 9.1837
Minimum possible area of triangle B = 7.0313

$Delta s A and B$ are similar.

To get the maximum area of $Delta B$ , side 5 of $Delta B$ should correspond to side 7 of $Delta A$ .

Sides are in the ratio 5 : 17
Hence the areas will be in the ratio of $5^2 : 7^2 = 25 : 49$

Maximum Area of triangle $B =( 18 * 25) / 49= 9.1837$

Similarly to get the minimum area, side 8 of $Delta A$ will correspond to side 5 of $Delta B$ .
Sides are in the ratio $5 : 8$ and areas $25 : 64$

Minimum area of $Delta B = (18*25)/64= 7.0313$

Triangle A has an area of 18 1818 and two sides of lengths 8 88 and 7 77 . Triangle B is similar to triangle A and has a side of length 5 55 . What are the maximum and minimum possible areas of triangle B?