Triangle A has an area of #9 # 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?

1 Answer
Dec 7, 2017

Maximum area 56.25 and Minimum area 41.3265

Explanation:

#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 =( 9 * 225) / 36= 56.25#

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 = (9*225)/49= 41.3265#