Question

solve for x.
8
16
20
a. 55
b. 65
c. 18
d. 12

Explanation:

Step1: Use similarity of triangles

Since the two triangles are similar, we have the proportion $\frac{x}{8}=\frac{20}{16}$.

Step2: Cross - multiply and solve

Cross - multiplying gives $16x = 8\times20$, so $16x=160$. Then $x = 10$. But this is wrong. Let's use another approach.
If we assume the triangles are similar and set up the correct proportion $\frac{x}{x + 8}=\frac{16}{20}$. Cross - multiplying: $20x=16(x + 8)$. Expand: $20x=16x+128$. Subtract $16x$ from both sides: $4x = 128$, so $x = 32$. Still wrong.
The correct proportion is $\frac{x}{20}=\frac{8}{16}$. Cross - multiply: $16x=8\times20$, $16x = 160$, $x = 10$.

Answer:

There seems to be an error in the options provided as the correct value of $x$ is $10$.