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Triangle A has an area of #27 # and two sides of lengths #8 # and #12 #. 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?

Answer 1

Allison Allen

Maximum area 60.75 and Minimum area 27

#Delta s A and B # are similar.

To get the maximum area of #Delta B#, side 12 of #Delta B# should correspond to side 8 of #Delta A#.

Sides are in the ratio 12 : 8 Hence the areas will be in the ratio of #12^2 : 8^2 = 144 : 64#

Maximum Area of triangle #B =( 27 * 144) / 64= 60.75#

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

Minimum area of #Delta B = (27*144)/144= 27#

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Answer 2

Autumn Armstrong

The maximum possible area of triangle B is (108) square units, and the minimum possible area of triangle B is (54) square units.

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Answer from HIX Tutor

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