Explanation:
In each case, use similar triangles to write a proportion.
If it helps, draw each triangle separately, with the right angles in the same position.
7. Write a proportion between the smaller triangles:
5 / 8 = 8 / (x−5)
64 = 5 (x−5)
12.8 = x−5
x = 17.8
9. Write a proportion between the top triangle and the big triangle:
x / 4 = 4 / (x+6)
16 = x (x+6)
16 = x² + 6x
0 = x² + 6x − 16
0 = (x−2) (x+8)
x = 2
11. Write a proportion between the smaller triangles:
3 / 4 = 4 / x
16 = 3x
x = 5.33
13. Write a proportion between the top triangle and the big triangle:
3 / x = x / (3+4)
x² = 21
x = 4.58