Question

Find x and y
x = ?
y = ?

Answer 1

Part 1)
`x=1.25\ units`

Part 2)
`y=1.75\ units`

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

`(5)/(5+x)=(8)/(10)`

solve for x

`5(10)=8(5+x)\\50=40+8x\\8x=50-40\\8x=10`

`x=(10)/(8)=1.25\ units`

Find the value of y

`(7)/(7+y)=(8)/(10)`

solve for y

`7(10)=8(7+y)\\70=56+8y\\8y=70-56\\8y=14`

`y=(14)/(8)=1.75\ units`