Answer:
The length of XY = 20
Step-by-step explanation:
Similar Triangles: Two triangles are said to be similar to one another if the have equal corresponding angles and proportionate sides.
Now, here ΔABC ~ ΔXYZ
Hence, by definition, the corresponding sides are proportionate to each other.
⇒[tex]\frac{AB}{XY} = \frac{BC}{YZ} = \frac{AC}{XZ}[/tex]
Here, AB =10,BC = 7, YZ = 14
Let length of XY = K
⇒[tex]\frac{10}{K} = \frac{7}{14}[/tex]
or, K = 20
So, the length of XY = 20
The length of XY is 20
Since the triangles are similar, we have the following equivalent ratio
AB : BC = XY : YZ
Substitute known values
10 : 7 = XY: 14
Multiply the left hand side by 2
20 :14 = XY: 14
By comparison, we have:
XY = 20
Hence, the length of XY is 20
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