Question

find x. 21/2 56/3 54/7 11

Explanation:

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

If a line is parallel to one side of a triangle and intersects the other two sides, then it divides those sides proportionally. So, \(\frac{12}{12 + 14}=\frac{9}{9 + x}\).

Step2: Cross - multiply

\(12(9 + x)=9(12 + 14)\).

Step3: Expand both sides

\(108+12x = 9\times26\), which simplifies to \(108 + 12x=234\).

Step4: Solve for \(x\)

Subtract \(108\) from both sides: \(12x=234 - 108\), so \(12x = 126\). Then \(x=\frac{126}{12}=\frac{21}{2}\).

Answer:

\(\frac{21}{2}\)