Question

quadrilateral tuvw is dilated by a scale factor of \\(\frac{2}{3}\\) to form quadrilateral tuvw. what is the measure of side wt?\
image of quadrilateral tuvw with sides: wt = 28, tu = 19.8, uv = 31.3, vw = 31.3

Explanation:

Step1: Recall dilation property

Dilation scales lengths by scale factor. Let original side (WT) be \( x \), dilated side \( W'T' = 28 \), scale factor \( k=\frac{2}{3} \). So \( W'T' = k \times WT \).

Step2: Solve for WT

Rearrange formula: \( WT=\frac{W'T'}{k} \). Substitute \( W'T' = 28 \), \( k=\frac{2}{3} \). So \( WT = 28\div\frac{2}{3}=28\times\frac{3}{2}=42 \).

Answer:

42