Question

the triangles below are similar. find the value of x. the image is not to scale.

Explanation:

Step1: Use the property of similar triangles

For similar triangles, the ratios of corresponding sides are equal.
$$\frac{CF}{CB}=\frac{FD}{CA}=\frac{ED}{BA}$$
We use \(\frac{CF}{CB}=\frac{ED}{BA}\)

Step2: Substitute the known values

Given \(CF = 16\), \(ED=20\), \(BA = 25\), and \(CB=x\)
Substitute into \(\frac{CF}{CB}=\frac{ED}{BA}\), we get \(\frac{16}{x}=\frac{20}{25}\)

Step3: Cross - multiply

Cross - multiply gives \(20x=16\times25\)

Step4: Solve for \(x\)

First, calculate \(16\times25 = 400\), then \(x=\frac{400}{20}\)

Answer:

\(x = 20\)