Triangle A has sides of lengths #32 #, #36 #, and #16 #. 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
Feb 13, 2018

Case 1 : #Delta B = color(green)(8, 18, 16#

case 2 : #Delta B = color(brown)(8, 9, 4#

Case 3 : #Delta B = color(blue)(8, 32/9. 64/9#

Explanation:

Case 1 : side 8 of triangle B corresponding to side 16 in triangle A

#8 / 16 = b / 36 = c / 32#

#b = (cancel(36)^color(green)18 * cancel8) / cancel16^color(red)cancel2#

#b = 18,

#c = (cancel(32)^color(green)16 * cancel8) / cancel16^color(red)cancel2#

# c = 16#

Similarly,Case 2 : side 8 of triangle B corresponding to side 32 in triangle A

#8 / 32 = b / 36 = c / 16#

#b = 9, c = 4#

Case 3 : side 8 of triangle B corresponding to side 36 in triangle A

#8 / 36 = b / 16 = c / 32#

#b = 32/9, c = 64/9#