Question

what are the values of m and y? (triangles are not drawn to scale.)

Explanation:

Step1: Determine the similarity of 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: Set up the proportion for side lengths

For similar triangles, the ratios of corresponding side lengths are equal.
We have \(\frac{AB}{ED}=\frac{BC}{DC}=\frac{AC}{EC}\). Given \(AB = 7\), \(ED=28\), \(BC = 9\), \(AC = 10\), \(DC=m\), \(EC=y\).
The ratio of similarity \(k=\frac{AB}{ED}=\frac{7}{28}=\frac{1}{4}\).

Step3: Find the value of \(m\)

Using \(\frac{BC}{DC}=\frac{AB}{ED}\), substituting the values: \(\frac{9}{m}=\frac{7}{28}\). Cross - multiply gives \(7m=9\times28\). Then \(m=\frac{9\times28}{7}=36\).

Step4: Find the value of \(y\)

Using \(\frac{AC}{EC}=\frac{AB}{ED}\), substituting the values: \(\frac{10}{y}=\frac{7}{28}\). Cross - multiply gives \(7y = 10\times28\). Then \(y=\frac{10\times28}{7}=40\).

Answer:

\(m = 36\)
\(y = 40\)