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

Answer:

Maximum area of triangle B = 103.68

Minimum area of triangle B = 32

Explanation:

#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 =( 18 * 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 = (18*144)/81 = 32#

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