Triangle A has an area of #4 # and two sides of lengths #6 # and #3 #. Triangle B is similar to triangle A and has a side with a length of #9 #. What are the maximum and minimum possible areas of triangle B?

1 Answer
sankarankalyanam
Oct 16, 2017

Largest possible area 36
Smallest possible area 16

Explanation:

Maximum possible are when side with length 9 in triangle B is the side similar to length 3 in Triangle A.
Area of triangles will be proportional in square of sides.

#:. # Area of triangle #B = (9/3)^2*4=36

For minimum possible area, side with length 9 is proportional to side with length 6 in triangle A.

#:.# Area of triangle #B = (6/3)^2*4=16#.

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