Question

in the trapezoid below, \\( \overline{tu} \\) is parallel to \\( \overline{qr} \\). if \\( qs = 35 \\), \\( ts = 15 \\), \\( qr = 28 \\), and \\( sr = 21 \\), find the length of \\( \overline{su} \\). figures are not necessarily drawn to scale. answer attempt 1 out of 2 \\( su = \\) submit answer

Explanation:

Step1: Identify Similar Triangles

Since \( \overline{TU} \parallel \overline{QR} \), \( \triangle QSR \sim \triangle TSU \) by the AA (Angle-Angle) similarity criterion (alternate interior angles are equal).

Step2: Set Up Proportion

For similar triangles, the ratios of corresponding sides are equal. So, \( \frac{QS}{TS} = \frac{SR}{SU} \).

We know \( QS = 35 \), \( TS = 15 \), and \( SR = 21 \). Let \( SU = x \). Then:
\[
\frac{35}{15} = \frac{21}{x}
\]

Step3: Solve for \( x \)

Cross - multiply: \( 35x = 15\times21 \)
Calculate \( 15\times21 = 315 \), so \( 35x = 315 \)
Divide both sides by 35: \( x=\frac{315}{35}=9 \)

Answer:

\( 9 \)