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Triangle A has sides of lengths #36 ,24 #, 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?

Answer 1

Sadie Adams

Triangle A: 36, 24, 16
Triangle B: #8,16/3,32/9#
Triangle B: #12, 8, 16/3#
Triangle B: # 18, 12, 8#

From the given Triangle A: 36, 24, 16

Use ratio and proportion

Let x, y, z be the sides respectively of triangle B proportional to triangle A

Case 1.

If x=8 in triangle B, solve y #y/24=x/36#

#y/24=8/36# #y=24*8/36# #y=16/3#

If x=8 solve z #z/16=x/36# #z/16=8/36# #z=16*8/36# #z=32/9# ~~~~~~~~~~~~~~~~~~~~~~~ Case 2.

if y=8 in triangle B solve x #x/36=y/24# #x/36=8/24# #x=36*8/24# #x=12#

If y=8 in triangle B solve z #z/16=y/24# #z/16=8/24# #z=16*8/24# #z=16/3# ~~~~~~~~~~~~~~~~~~~~~~~ Case 3.

if z=8 in triangle B, solve x #x/36=z/16# #x/36=8/16# #x=36*8/16# #x=18#

if z=8 in triangle B, solve y #y/24=z/16# #y/24=8/16# #y=24*8/16# #y=12#

God bless....I hope the explanation is useful.

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Answer 2

Allison Allen

The possible lengths of the other two sides of triangle B are 12 and 16.

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.