Triangle A has an area of #8 # and two sides of lengths #8 # and #7 #. Triangle B is similar to triangle A and has a side with a length of #16 #. What are the maximum and minimum possible areas of triangle B?

1 Answer
Leland Adriano Alejandro
Mar 25, 2016

Maximum Area #=361.28" "#square units
Minimum Area #=9.29514" "#square units

Explanation:

I computed all possible triangles and there are 2 possible triangles for A and 6 possible triangles for B. Then I computed the area for each triangle to determine the maximum and minimum areas.

For first triangle A:
sides #a=8# , #b=7# , #c=2.3809" "#,angle #C=16.6015^@#

For first triangle B:
sides #a'=16#, #" "b'=14#, #" "c'=4.76182#,angle #C=16.6015^@#,
Area#=32#

sides #a''=128/7#,#" "b''=16#, #" "c''=5.44208#,angle #C=16.6015^@#,
Area#=41.7959#

sides #a'''=53.7609#,#" "b'''=47.0408#,#" "c'''=16#,angle #C=16.6015^@#,
Area#=361.28" "#Maximum Area
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
For second triangle A:
sides #a=8# , #b=7# , #c=14.8436" "#,angle #C=163.398^@#

For first triangle B:
sides #a'=16#, #" "b'=14#, #" "c'=29.6871#,angle #C=163.398^@#,
Area#=32#

sides #a''=128/7#,#" "b''=16#, #" "c''=33.9281#,
angle #C=163.398^@#,
Area#=41.798#

sides #a'''=8.62327#,#" "b'''=7.54536#,#" "c'''=16#,
angle #C=163.398^@#,
Area#=9.29514" "#Minimum Area

God bless....I hope the explanation is useful.

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