Question

what values of v and w make \\( \triangle rst \cong \triangle ced \\)?

Explanation:

Step1: Use the property of congruent triangles

Since \(\triangle{RST}\cong\triangle{CED}\), their corresponding sides are equal. So we have the following two - equations:
\(w + 38=20w\) (because \(SR = ED\)) and \(6w + v-1=4v+w\) (because \(RT = CD\))

Step2: Solve the first equation for \(w\)

For \(w + 38=20w\), subtract \(w\) from both sides:
\(38=20w - w\)
\(38 = 19w\)
Divide both sides by \(19\): \(w=\frac{38}{19}=2\)

Step3: Substitute \(w = 2\) into the second equation and solve for \(v\)

Substitute \(w = 2\) into \(6w + v-1=4v+w\)
\(6\times2+v - 1=4v+2\)
\(12 + v-1=4v+2\)
\(11 + v=4v+2\)
Subtract \(v\) from both sides: \(11=4v+2 - v\)
\(11 = 3v+2\)
Subtract \(2\) from both sides: \(3v=11 - 2\)
\(3v=9\)
Divide both sides by \(3\): \(v = 3\)

Answer:

\(v = 3\), \(w = 2\)