Answer:
D) x = 40.5
Step-by-step explanation:
When parallel lines create a smaller triangle inside a larger triangle, the triangles are similar. Triangle similarity means that side lengths are proportional, meaning to find x we must use dimensions of the smaller triangle to create a proportion.
The left side of the larger triangle is 12 + 15, so it is 27.
The left side of the smaller triangle is 12.
So, part of the proportion will be [tex]\frac{27}{12}[/tex]
The bottom side of the larger triangle is x.
The bottom side of the smaller triangle is 18.
So, part of the proportion will be [tex]\frac{x}{18}[/tex]
The full proportion will be:
[tex]\frac{27}{12}=\frac{x}{18}[/tex]
Cross multiply and solve for x.
27(18) = 12x
486 = 12x
40.5 = x
