Triangle A has sides of lengths #54 #, #44 #, and #64 #. Triangle B is similar to triangle A and has a side of length #4 #. What are the possible lengths of the other two sides of triangle B?

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Answer 1 · 2017-02-07T04:49:38

# <4,3 7/27, 4 20/27>#, # <4 10/11,4, 5 9/11># and# <3 3/8, 2 3/4,4>#

Let #( 4, a , b)# are the lengths of Triangle B..

A. Comparing 4 and 54 from Triangle A,

#b/44=4/54#, #b=2/27*44=3 7/27#

#c/64=4/54#, #c=2/27*64=4 20/27#

The length of sides for Triangle B is# <4,3 7/27, 4 20/27>#

B. Comparing 4 and 44 from Triangle A,

#b/54=4/44#, #b=1/11*54=4 10/11#

#c/64=4/44#, #c=1/11*64=5 9/11#

The length of sides for Triangle B is# <4 10/11,4, 5 9/11>#

Comparing 4 and 64 from Triangle A,

#b/54=4/64#,#b =1/16*54=3 3/8#

#c/44=4/64#, #c=1/16*44= 2 3/4#
The length of sides for Triangle B is# <3 3/8, 2 3/4,4>#

Therefore the possible sides for Triangle B are

# <4,3 7/27, 4 20/27>#, # <4 10/11,4, 5 9/11># and# <3 3/8, 2 3/4,4>#