Question

find sw.
sw = \square

Explanation:

Step1: Identify Similar Triangles

Since \( UW \parallel ST \) (implied by the red arrows, indicating parallel lines), triangles \( VUW \) and \( VST \) are similar by the Basic Proportionality Theorem (Thales' theorem). Thus, the ratios of corresponding sides are equal: \(\frac{VU}{VT}=\frac{VW}{VS}\).

Step2: Calculate \( VU \)

Given \( VT = 63 \) and \( UT = 28 \), we find \( VU=VT - UT=63 - 28 = 35 \).

Step3: Set Up Proportion

Let \( SW = x \), then \( VW = 90 - x \) and \( VS = 90 \). From the similarity of triangles: \(\frac{VU}{VT}=\frac{VW}{VS}\), substituting values: \(\frac{35}{63}=\frac{90 - x}{90}\).

Step4: Solve for \( x \)

Cross - multiply: \( 35\times90 = 63\times(90 - x) \)
\( 3150=5670 - 63x \)
Add \( 63x \) to both sides: \( 63x + 3150 = 5670 \)
Subtract \( 3150 \) from both sides: \( 63x=5670 - 3150 = 2520 \)
Divide both sides by \( 63 \): \( x=\frac{2520}{63}=40 \)

Answer:

\( 40 \)