1. For triangle ABC, the value of 'x' and 'y' are 15 and 20 respectively.
2. For triangle XYZ, the value of 'x' and 'y' are 17 and 8 respectively.
What is a triangle?
A triangle is a two-dimensional geometrical figure that has three sides, three interior angles, and three vertices.
1. ΔABC and ΔXYZ are similar.
Therefore, \(\frac{AB}{XY} = \frac{25}{10}\)
⇒ \(\frac{AB}{XY} = 2.5\)
Here, \(AC = x, XZ = 6\)
Therefore, \(\frac{AC}{XZ} = 2.5\)
⇒ \(AC = 2.5(XZ)\)
⇒ \(x = (2.5)(6)\)
⇒ \(x = 15\)
Again, \(CB = y, ZY = 8\)
\(\frac{CB}{ZY}= 2.5\)
⇒ \(\frac{y}{8} = 2.5\)
⇒ \(y = (2.5) (8)\)
⇒ \(y = 20\)
2. For ΔABC
BC
\(= \sqrt{AB^{2} - AC^{2}}\\= \sqrt{34^{2} - 16^{2}}\\= \sqrt{900}\\= 30\)(Side can't be negative.)
Here, ΔABC and ΔXYZ are similar.
Therefore,
\(\frac{BC}{ZY}\\= \frac{30}{15}\\= 2\)
Now, \(AB = 34, XY = x\)
Therefore, \(\frac{AB}{XY} = 2\)
⇒ \(\frac{34}{x} = 2\)
⇒ \(x = \frac{34}{2}\)
⇒ \(x = 17\)
Again, \(AC = 16, XZ = y\)
Therefore, \(\frac{AC}{XZ} = \frac{16}{y} = 2\)
⇒ \(\frac{16}{y} = 2\)
⇒ \(y = \frac{16}{2}\)
⇒ \(y = 8\)
Learn more about a triangle here: https://brainly.com/question/2338119
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