Question

solve for x. figures are not necessarily drawn to scale.
answer attempt 2 out of 2
x =

Explanation:

Step1: Use the similarity of triangles

Since \(\triangle EDF\) and \(\triangle CDB\) are similar (by AA similarity, as the vertical angles at \(D\) are equal and the angles formed by the parallel - like arrows are equal). For similar triangles, the ratios of corresponding sides are equal. So, \(\frac{ED}{CD}=\frac{FD}{BD}\). Substituting the given values, we get \(\frac{x}{3.2}=\frac{3}{2.4}\).

Step2: Solve the proportion for \(x\)

Cross - multiply the proportion \(\frac{x}{3.2}=\frac{3}{2.4}\). We have \(2.4x = 3\times3.2\). Then \(2.4x=9.6\). Divide both sides by \(2.4\): \(x=\frac{9.6}{2.4}\).

Answer:

\(x = 4\)