Triangle A has an area of #4 # and two sides of lengths #8 # and #3 #. Triangle B is similar to triangle A and has a side with a length of #8 #. What are the maximum and minimum possible areas of triangle B?

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Answer 1 · 2017-10-13T03:54:27

Minimum possible area o B 4
Maximum possible area of B 28(4/9) or 28.44

Since the triangles are similar, sides are in same proportion.

Case (1) Minimum possible area
#8/8=a/3 or a=3# Sides are 1:1
Areas will be square of the sides ratio #=1^2=1#
#:. Area Delta B = 4#

Case (2) Maximum possible area
#8/3=a/8 or a=64/3# Sides are 8:3
Areas will be #(8/3)^2=64/9#
#:. Area Delta B =(64/9)*4=256/9=28(4/9)#