Triangle A has an area of #4 # and two sides of lengths #8 # and #7 #. Triangle B is similar to triangle A and has a side with a length of #13 #. What are the maximum and minimum possible areas of triangle B?

1 Answer
sankarankalyanam
Dec 7, 2017

#Delta s A and B # are similar.

To get the maximum area of #Delta B#, side 13 of #Delta B# should correspond to side 7 of #Delta A#.

Sides are in the ratio 13 : 7
Hence the areas will be in the ratio of #13^2 : 7^2 = 625 : 49#

Maximum Area of triangle #B =( 4 * 169) / 49= 13.7959#

Similarly to get the minimum area, side 8 of #Delta A # will correspond to side 13 of #Delta B#.
Sides are in the ratio # 13 : 8# and areas #169 : 64#

Minimum area of #Delta B = (4*169)/64= 10.5625#

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