Question

which equation correctly solves for x?
\frac{18}{15}=\frac{x}{12}
\frac{15}{18}=\frac{x}{12}
\frac{15}{18}=\frac{12}{x}

Explanation:

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

If a line is drawn parallel to one side of a triangle intersecting the other two sides, then it divides those sides proportionally.
Here, the line divides the sides \(EK = 15\), \(EJ=18\) and \(KH = x\), \(HS = 12\) proportionally. So, \(\frac{EK}{EJ}=\frac{KH}{HS}\).

Step2: Substitute the values

Substituting \(EK = 15\), \(EJ = 18\), \(KH=x\) and \(HS = 12\) into the proportion \(\frac{EK}{EJ}=\frac{KH}{HS}\), we get \(\frac{15}{18}=\frac{x}{12}\).

Answer:

\(\frac{15}{18}=\frac{x}{12}\) (the second option)