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Triangle A has an area of #4 # and two sides of lengths #12 # and #7 #. Triangle B is similar to triangle A and has a side with a length of #5 #. What are the maximum and minimum possible areas of triangle B?

Answer 1

Savannah Aguilar

Maximum possible area of triangle B = 2.0408
Minimum possible area of triangle B = 0.6944

#Delta s A and B # are similar.

To get the maximum area of #Delta B#, side 5 of #Delta B# should correspond to side 7 of #Delta A#.

Sides are in the ratio 5 : 7 Hence the areas will be in the ratio of #5^2 : 7^2 = 25 : 49#

Maximum Area of triangle #B =( 4 * 25) / 49= 2.0408#

Similarly to get the minimum area, side 12 of #Delta A # will correspond to side 5 of #Delta B#. Sides are in the ratio # 5 : 12# and areas #25 : 144#

Minimum area of #Delta B = (4*25)/144= 0.6944#

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