Answer:
Part 1) [tex]x=1.25\ units[/tex]
Part 2) [tex]y=1.75\ units[/tex]
Step-by-step explanation:
In this problem
the triangles of the figure are similar by AA Similarity Theorem
Remember that
If two figures are similar, then the ratio of its corresponding sides is proportional and its corresponding angles are congruent
so
Applying proportion
Find the value of x
[tex]\frac{5}{5+x}=\frac{8}{10}[/tex]
solve for x
[tex]5(10)=8(5+x)\\50=40+8x\\8x=50-40\\8x=10[/tex]
[tex]x=\frac{10}{8}=1.25\ units[/tex]
Find the value of y
[tex]\frac{7}{7+y}=\frac{8}{10}[/tex]
solve for y
[tex]7(10)=8(7+y)\\70=56+8y\\8y=70-56\\8y=14[/tex]
[tex]y=\frac{14}{8}=1.75\ units[/tex]
