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Triangle A has sides of lengths #51 #, #45 #, and #54 #. Triangle B is similar to triangle A and has a side of length #3 #. What are the possible lengths of the other two sides of triangle B?

Answer 1

Sadie Allen

See below.

For similar triangles we have:

#A/B=(A')/(B')color(white)(888888)# # A/C=(A')/(C')# etc.

Let #A=51 , B=45 , C=54#

Let #A'=3#

#A/B=51/45=3/(B')=>B'=45/17#

#A/C=51/54=3/(C')=>C'=54/17#

1st set of possible sides: #{3,45/17,54/17}#

Let #B'=3#

#A/B=51/45=(A')/3=>A'=17/5#

#B/C=45/54=3/(C')=>C'=18/5#

2nd set of possible sides #{17/5,3,18/5}#

Let #C'=3#

#A/C=51/54=(A')/3=>A'=17/6#

#B/C=45/54=(B')/3=>B'=5/2#

3rd set of possible sides #{17/6,5/2,3}#

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