Question

find the value of vt

Explanation:

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

Since \( UV\parallel RS\), we have \(\frac{SV}{VT}=\frac{RU}{UT}\). Substituting the given values: \(\frac{3x - 3}{x + 2}=\frac{14}{6}\).

Step2: Cross - multiply

Cross - multiplying gives \(6(3x - 3)=14(x + 2)\).
Expanding both sides: \(18x-18 = 14x + 28\).

Step3: Solve for \(x\)

Subtract \(14x\) from both sides: \(18x-14x-18=14x-14x + 28\), so \(4x-18 = 28\).
Add \(18\) to both sides: \(4x=28 + 18\), \(4x=46\), then \(x=\frac{46}{4}=\frac{23}{2}\).

Step4: Find \(VT\)

Substitute \(x = \frac{23}{2}\) into \(VT=x + 2\).
\(VT=\frac{23}{2}+2=\frac{23 + 4}{2}=\frac{27}{2}=13.5\).

Answer:

\(13.5\)