Triangle A has sides of lengths #60 #, #42 #, and #54 #. 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 · 2018-01-28T08:38:49

Possible lengths of two triangles are

Case 1 : #color(green)(A (42, 54, 60) & B (7. 8.2727, 10))#

Case 2 : #color(brown)(A (42, 54, 60) & B (5.4444, 7, 7.7778))#

Case 3 :# color(blue)( A (42, 54, 60) & B (4.9, 6.3, 7))#

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Let the two triangles A & B have sides PQR & XYZ respectively.

#(PQ ) / (XY) = (QR) / (YZ) = (RP) / (ZX)#

Case 1 : Let XY = # color(green)(7)#

#42 / 7 = 54 / (YZ) = 60 / (ZX)#

#YZ = (54 * 7) / 42 = color(green)(8.2727)#

#ZX = (60 * 7) / 42 = color(green)(10)#

Case 2 : Let YZ = #color(brown)7#

#42 / (XY) = 54 / 7 = 60 / (ZX)#

#XY = (42 * 7) / 54 = color(brown)(5.4444)#

#ZX = (60 * 7) / 54 = color(brown)(7.7778)#

Case 3 : Let ZX = #color(blue)7#

#42 / (XY) = 54 / YZ = 60 /7#

#XY = (42 * 7) / 60 = color(blue)(4.9)#

#YZ = (54 * 7) / 60 = color(blue)(6.3)#