Triangle A has sides of lengths #54 #, #44 #, and #64 #. Triangle B is similar to triangle A and has a side of length #8 #. What are the possible lengths of the other two sides of triangle B?

1 Answer
Jim G.
Apr 3, 2016

#(8,176/27,256/27) , (108/11,8,128/11) , (27/4,11/2,8)#

Explanation:

Since the triangles are similar then the ratios of corresponding sides are equal.

Name the 3 sides of triangle B , a , b and c , corresponding to the sides 54 , 44 and 64 in triangle A.
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If side a = 8 then ratio of corresponding sides = #8/54 = 4/27 #

Hence b = # 44xx4/27 = 176/27" and " c = 64xx4/27 = 256/27 #

The 3 sides in B # = (8,176/27,256/27 ) #
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If side b = 8 then ratio of corresponding sides# = 8/44 = 2/11 #

hence a = # 54xx2/11 = 108/11" and " c = 64xx2/11 = 128/11 #

The 3 sides in B = #(108/11,8,128/11 )#
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If side c = 8 then ratio of corresponding sides #= 8/64 = 1/8 #

hence a #=54xx1/8 = 27/4" and " b = 44xx1/8 = 11/2 #

The 3 sides in B =# (27/4,11/2,8 )#
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