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Triangle A has an area of #27 # and two sides of lengths #8 # and #6 #. 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?

1 Answer

Answer:

maximum possible area of triangle B #=48# &

minimum possible area of triangle B #=27#

Explanation:

Given area of triangle A is

#\Delta_A=27#

Now, for maximum area #\Delta_B# of triangle B, let the given side #8# be corresponding to the smaller side #6# of triangle A.

By the property of similar triangles that the ratio of areas of two similar triangles is equal to the square of ratio of corresponding sides then we have

#\frac{\Delta_B}{\Delta_A}=(8/6)^2#

#\frac{\Delta_B}{27}=16/9#

#\Delta_B=16\times 3#

#=48#

Now, for minimum area #\Delta_B# of triangle B, let the given side #8# be corresponding to the greater side #8# of triangle A.

The ratio of areas of similar triangles A & B is given as

#\frac{\Delta_B}{\Delta_A}=(8/8)^2#

#\frac{\Delta_B}{27}=1#

#\Delta_B=27#

Hence, the maximum possible area of triangle B #=48# &

the minimum possible area of triangle B #=27#