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Triangle A has an area of #12 # and two sides of lengths #6 # 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?

Answer 1

Autumn Armstrong

Maximum area 48 and Minimum area 21.3333**

#Delta s A and B # are similar.

To get the maximum area of #Delta B#, side 12 of #Delta B# should correspond to side 6 of #Delta A#.

Sides are in the ratio 12 : 6 Hence the areas will be in the ratio of #12^2 : 6^2 = 144 : 36#

Maximum Area of triangle #B =( 12 * 144) / 36= 48#

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 = (12*144)/81= 21.3333#

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Answer 2

James Atkins

The maximum possible area of triangle B is ( 72 ) square units, and the minimum possible area is ( 36 ) square units.

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Answer from HIX Tutor

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