Triangle A has sides of lengths #36 #, #42 #, and #60 #. Triangle B is similar to triangle A and has a side of length #7 #. What are the possible lengths of the other two sides of triangle B?

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Answer 1 · 2016-06-20T18:40:19

#{color(white)(2/2)color(magenta)(7)" ; "color(blue)(8.16bar6-> 8 1/6)" ; "color(brown)(11.6bar6->11 2/3)color(white)(2/2)}#

#{color(white)(2/2)color(magenta)(7)" ; "color(blue)(6)" ; "color(brown)(10)color(white)(2/2)}#

#{color(white)(2/2)color(magenta)(7)" ; "color(blue)(4.2->4 2/10)" ; "color(brown)(4.9->4 9/10)color(white)(2/2)}#

Let the unknown sides of triangle B be b and c

The by ratio:

#color(blue)("Condition 1")#

#7/36=b/42=c/60#

#=># The other two side lengths are:

#b=(7xx42)/36 ~~ 8.16bar6# approximate value
#c=(7xx60)/36~~11.66bar6# approximate value

'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

#color(blue)("Condition 2")#

#7/42=b/36=c/60#

#=># The other two side lengths are:

#b=(7xx36)/42=6#
#c=(7xx60)/42=10#
'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
#color(blue)("Condition 3")#

#7/60=b/36=c/42#

#b=(7xx36)/60=4.2#
#c=(7xx42)/60=4.9#
'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
#color(blue)("Determine exact values for condition 1")#

#10b~~81.66bar6#
#100b~~816.66bar6#

#100b-10b=735#

#90b=735#

#b=735/90=8 1/6#
,.......................................................

#color(white)(..)c~~color(white)(.)11.66bar6#
#10c~~116.66bar6#

#10c-c=105#

#9c=105#

#c=105/9=11 2/3#