If △AYB∼△XYZ , and AB=5 , AY=12 , AY=AX , and BY=BZ , then what is the length of BZ ? Enter your response as a mixed fraction if needed.

Answer 1

Since the two triangles △AYB and △XYZ are similar, their corresponding sides are proportional. Thus, we can write the following ratios:

AY/XY = AB/XZ
12/XY = 5/XZ

Since AY = AX, we can substitute that into the equation:

12/XY = 5/XZ
12/XY = 5/AY
12/XY = 5/12
12/5 = XY/12
144 = 5XY
XY = 144/5

Now, since BY = BZ, we can substitute that into the equation:

BY/ZZ = AB/XZ
BY/BZ = 5/XZ
BY/BY = 5/XZ
1 = 5/XZ
XZ = 5

Now we can find the value of BZ:

XY + YZ = XZ
144/5 + YZ = 5
YZ = 5 - 144/5
YZ = 25/5 - 144/5
YZ = (25 - 144)/5
YZ = -119/5

Therefore, the length of BZ is -119/5.