Question

find rs.
rs =
submit
work it out

Explanation:

Step1: Identify Similar Triangles

From the diagram, \( SP \parallel RQ \) (implied by the red arrows, so by the Basic Proportionality Theorem or AA similarity, \( \triangle TSP \sim \triangle TRQ \)). Let \( RS = x \), so \( TR = TS + SR = 38 + x \). The bases: \( TP = TQ - PQ = 33 - 11 = 22 \), \( TQ = 33 \).

Step2: Set Up Proportion

By similarity, \( \frac{TS}{TR} = \frac{TP}{TQ} \). Substitute values: \( \frac{38}{38 + x} = \frac{22}{33} \). Simplify \( \frac{22}{33} = \frac{2}{3} \), so \( \frac{38}{38 + x} = \frac{2}{3} \).

Step3: Solve for \( x \)

Cross - multiply: \( 3\times38 = 2\times(38 + x) \). \( 114 = 76 + 2x \). Subtract 76: \( 2x = 114 - 76 = 38 \). Divide by 2: \( x = 19 \).

Answer:

\( 19 \)