SOLUTION: The triangles ABC and XYZ are similar. The side AB is 5 cm long. The sides BC and YZ are 7 cm and 3 cm longer than the side XY, respectively. Find the length of XY.

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Question 1170888: The triangles ABC and XYZ are similar. The side AB is 5 cm long. The sides BC and
YZ are 7 cm and 3 cm longer than the side XY, respectively. Find the length of XY.
Found 2 solutions by ikleyn, MathTherapy:
Answer by ikleyn(52754) About Me  (Show Source):
Answer by MathTherapy(10549) About Me  (Show Source):
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The triangles ABC and XYZ are similar. The side AB is 5 cm long. The sides BC and
YZ are 7 cm and 3 cm longer than the side XY, respectively. Find the length of XY.
.
Let XY = z
With the 2 Δs being SIMILAR, AB and BC correspond to XY and YZ, respectively
Since BC is 7 cm longer than XY, then BC = XY + 7, or z + 7
Also, since YZ is 3 cm longer than XY, then YZ = XY + 3, or z + 3
With BC being LONGER (XY + 7, or z + 7) than YZ (XY + 3, or z + 3), obviously ΔABC is the LARGER of the 2

matrix%281%2C3%2C+AB%2FXY+=+BC%2FYZ%2C+or%2C+AB%2FBC+=+XY%2FYZ%29
AB%2FXY+=+%28XY+%2B+7%29%2F%28XY+%2B+3%29 <==== Using the former SIMILARITY-PROPORTION
5%2Fz+=+%28z+%2B+7%29%2F%28z+%2B+3%29 
z%28z+%2B+7%29+=+5%28z+%2B+3%29 ---- Cross-multiplying
z%5E2+%2B+7z+=+5z+%2B+15
z%5E2+%2B+2z++-++15+=+0
(z - 3)(z + 5) = 0 
z(XY) = 3 cm       OR       z = - 5 (ignore)