Answer:
x=9 and w=12
Step-by-step explanation:
To solve for w and x, create proportions between the two similar triangles.
[tex]\frac{Big Side}{Big Side} =\frac{little side}{little side}[/tex]
where Big represents the bigger triangle an little represents the smaller triangle.
[tex]\frac{8}{16}=\frac{w}{12+w}[/tex]
Cross multiply and solve for w.
8(12+w)=16(w)
96 + 8w = 16w
96 + 8w - 8w = 16w - 8w
96 = 8w
w=12
Repeat with a new proportion.
[tex]\frac{8}{22}=\frac{12}{24+x}[/tex]
Cross multiply and solve for x.
8(24+x)=22(12)
192 + 8x = 264
8x = 72
x=9
