Question

in the following triangle, find length qt. round to the nearest tenth.

Explanation:

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

Since \(ST\parallel RQ\) (by the construction of the figure with right - angles), we can use the proportion \(\frac{QT}{QS}=\frac{QU}{QR}\). Let \(QT = x\), then \(QS=x + 4.8\), \(QU = 6.1\), and \(QR=6.1 + 9.2=15.3\). So the proportion is \(\frac{x}{x + 4.8}=\frac{6.1}{15.3}\).

Step2: Cross - multiply

Cross - multiplying gives \(15.3x=6.1(x + 4.8)\).
Expanding the right - hand side: \(15.3x=6.1x+6.1\times4.8\).
\(15.3x=6.1x + 29.28\).

Step3: Solve for \(x\)

Subtract \(6.1x\) from both sides: \(15.3x-6.1x=29.28\).
\(9.2x=29.28\).
Divide both sides by \(9.2\): \(x=\frac{29.28}{9.2}\).
\(x = 3.2\).

Answer:

\(3.2\)