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, [tex]\frac{AB}{XY} = \frac{25}{10}[/tex]
⇒ [tex]\frac{AB}{XY} = 2.5[/tex]
Here, [tex]AC = x, XZ = 6[/tex]
Therefore, [tex]\frac{AC}{XZ} = 2.5[/tex]
⇒ [tex]AC = 2.5(XZ)[/tex]
⇒ [tex]x = (2.5)(6)[/tex]
⇒ [tex]x = 15[/tex]
Again, [tex]CB = y, ZY = 8[/tex]
[tex]\frac{CB}{ZY}= 2.5[/tex]
⇒ [tex]\frac{y}{8} = 2.5[/tex]
⇒ [tex]y = (2.5) (8)[/tex]
⇒ [tex]y = 20[/tex]
2. For ΔABC
BC
[tex]= \sqrt{AB^{2} - AC^{2}}\\= \sqrt{34^{2} - 16^{2}}\\= \sqrt{900}\\= 30[/tex](Side can't be negative.)
Here, ΔABC and ΔXYZ are similar.
Therefore,
[tex]\frac{BC}{ZY}\\= \frac{30}{15}\\= 2[/tex]
Now, [tex]AB = 34, XY = x[/tex]
Therefore, [tex]\frac{AB}{XY} = 2[/tex]
⇒ [tex]\frac{34}{x} = 2[/tex]
⇒ [tex]x = \frac{34}{2}[/tex]
⇒ [tex]x = 17[/tex]
Again, [tex]AC = 16, XZ = y[/tex]
Therefore, [tex]\frac{AC}{XZ} = \frac{16}{y} = 2[/tex]
⇒ [tex]\frac{16}{y} = 2[/tex]
⇒ [tex]y = \frac{16}{2}[/tex]
⇒ [tex]y = 8[/tex]
Learn more about a triangle here: https://brainly.com/question/2338119
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