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Triangle A has an area of #3 # and two sides of lengths #6 # and #7 #. Triangle B is similar to triangle A and has a side of length #15 #. What are the maximum and minimum possible areas of triangle B?

Answer 1

James Atkins

Maximum area #18.75# and Minimum area #13.7755#

#Delta s A and B # are similar.

To get the maximum area of #Delta B#, side 15 of #Delta B# should correspond to side 6 of #Delta A#.

Sides are in the ratio 15 : 6 Hence the areas will be in the ratio of #15^2 : 6^2 = 225 : 36#

Maximum Area of triangle #B =( 3 * 225) / 36 = 18.75#

Similarly to get the minimum area, side 7 of #Delta A # will correspond to side 15 of #Delta B#. Sides are in the ratio # 15 : 7# and areas #225 : 49#

Minimum area of #Delta B = (3*225)/49= 13.7755#

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Answer 2

Noah Atkinson

The maximum possible area of Triangle B is ( 45 ), and the minimum possible area is ( 27 ).

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