Question

what are the values of m and w? (triangles are not drawn to scale.)
show your work here
m=
w=

Explanation:

Step1: Identify similar triangles

Since \(AB\parallel ED\), \(\triangle ABC\sim\triangle EDC\) (by the AA similarity criterion as \(\angle ABC=\angle EDC\) and \(\angle BAC = \angle DEC\) because of parallel lines).

Step2: Use the ratio of corresponding sides

For similar triangles \(\triangle ABC\) and \(\triangle EDC\), we have the proportion \(\frac{AB}{ED}=\frac{AC}{EC}=\frac{BC}{DC}\).
We know \(AB = 14\), \(ED=12\), \(EC = 15\), \(DC = 21\).
Using \(\frac{AB}{ED}=\frac{AC}{EC}\), substitute the values: \(\frac{14}{12}=\frac{m}{15}\).
Cross - multiply: \(12m=14\times15\).
\(12m = 210\), then \(m=\frac{210}{12}=\frac{35}{2}=17.5\).
Using \(\frac{AB}{ED}=\frac{BC}{DC}\), substitute the values: \(\frac{14}{12}=\frac{w}{21}\).
Cross - multiply: \(12w=14\times21\).
\(12w=294\), then \(w=\frac{294}{12}=\frac{49}{2}=24.5\).

Answer:

\(m = 17.5\), \(w=24.5\)