Triangle A has sides of lengths #36 #, #44 #, and #32 #. 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 · 2018-01-20T13:42:24

Possible lengths of other two sides of triangle B are

Case 1 : #4.8889, 3.5556#

Case 2 : #3.2727, 2.9091#

Case 3 : #4.5, 5.5#

Let the sides be a1, a2, a3 of #Delta#A and b1, b2, b3 of #Delta# B.

We know,

#(a1) / (b1) = (a2) / (b2) = (a3) / (b3)#

Given #a1 = 36, a2 = 44, a3 = 32#

Case 1 :
#b1 = 4#

Then #b2 = ((a2) * (b1)) / (a1) = (44*4)/36 = 4.8889#

#b3 = ((a3) * (b1)) / (a1) = (32 * 4) / 36 = 3.5556#

Case 2 :
#b2 = 4#

#b1 = ((a1)*(b2)) / (a2) = (36*4)/44 = 3.2727#

#b3 = (32 * 4) / 44 = 2.9091#

Case 3 :

#b3 = 4#

#b1 = (36 * 4) / 32 = 4.5#

#b2 = (44 * 4) / 32 = 5.5#