The ratio of corresponding sides is same for all the sides for similar triangles. The value [tex]x[/tex] is 17.5 units and value of [tex]y[/tex] is 19.2 units.
What are the properties of similar polygon?
Two polygons are said to be similar or congruent pentagon-
- The corresponding angle of two pentagons are congruent.
- The ratio of corresponding sides is same for all the sides.
Given information-
In the given figure,
[tex]\Delta ABC\cong \Delta AVW[/tex]
As for the similar triangle the ratios of corresponding sides is same for all the sides. Hence,
[tex]\dfrac{AB}{AV} =\dfrac{BC}{VW} =\dfrac{AC}{AW}[/tex]
Take two ratios to find [tex]x[/tex],
[tex]\dfrac{BC}{VW} =\dfrac{AC}{AW}[/tex]
Put the values,
[tex]\dfrac{16}{10} =\dfrac{28}{x}\\16x=280\\x=\dfrac{280}{16} \\x=17.5[/tex]
Take another two ratios to find [tex]y[/tex],
[tex]\dfrac{BC}{VW} =\dfrac{AB}{AV}[/tex]
Put the values,
[tex]\dfrac{16}{10} =\dfrac{y}{12}\\16\times12=10y\\y=\dfrac{192}{10} \\y=19.2[/tex]
Hence, the value [tex]x[/tex] is 17.5 units and value of [tex]y[/tex] is 19.2 units.
Learn more about the similar polygon here;
https://brainly.com/question/17756657
