Question

find the value of x.
x =

Explanation:

Step1: Use the basic proportionality theorem (Thales' theorem)

Since \(DE\parallel AC\), we have \(\frac{BE}{BC}=\frac{DE}{AC}\). Here, \(BE = 4\), \(BC=4+(x - 2)\), \(DE = 5\), and \(AC = 10\). So, \(\frac{4}{4+(x - 2)}=\frac{5}{10}\).

Step2: Simplify the equation

Simplify \(\frac{5}{10}=\frac{1}{2}\). The equation becomes \(\frac{4}{x + 2}=\frac{1}{2}\).

Step3: Cross - multiply

Cross - multiplying gives \(x+2=4\times2\).

Step4: Solve for \(x\)

\(x+2 = 8\), then \(x=8 - 2\).

Answer:

\(6\)