Question

Find x, y, and z with similar right triangles

Answer 1

Explanation:

Upon observing the triangles, it appears easier to find x first since we can set up the proportion: 10/20 = 20/ (x + 10) because the triangle with sides y, 10, and 20 is similar to the biggest triangle.

10/20 = 1/2 = 20/ (x + 10)

x + 10 = 2*20

x + 10 = 40

x = 30

Next we set up the equations for y and z. (x + 10)/ 20 = z/y = 40/20 = 2

and y/10 = z/ 20 ( same thing)...

30/y = y / 10 = z/20

Focus on 30/y = y /10 ... 30*10 = y*y

y*y = 300 or y = 10
`√(3)`

and z = 2y from z/y = 40/20

so z = 2* 10
`√(3)` ,

z = 20
`√(3)`

Conclusion: x = 30, y = 10
`√(3)` and z = 20
`√(3)`