Question

m.12 triangle proportionality theorem 6wa
find st.

st =

Explanation:

Step1: Calculate length of WS

First, find the length of segment WS. The total length VS is 36, and VW is 24.
$WS = VS - VW = 36 - 24 = 12$

Step2: Set up proportion via theorem

By the Triangle Proportionality Theorem, $\frac{ST}{UT} = \frac{WS}{VW}$. Let $ST = x$, so $UT = 50 - x$.
$\frac{x}{50 - x} = \frac{12}{24}$

Step3: Simplify and solve for x

Simplify the ratio and cross-multiply to solve for x.
$\frac{x}{50 - x} = \frac{1}{2}$
$2x = 50 - x$
$2x + x = 50$
$3x = 50$
$x = \frac{50}{3} \approx 16.67$

Answer:

$\frac{50}{3}$ or approximately 16.67