Question

what values of t and u make \\( \triangle vwx \cong \triangle efd \\)?

Explanation:

Step1: Set up equations from congruent sides

Since \(\triangle VWX\cong\triangle EFD\), the corresponding sides are equal.
For the sides \(VX\) and \(FD\): \(t + 48=7t\).
For the sides \(VW\) and \(FE\): \(u + 18=4u\).

Step2: Solve the equation for \(t\)

Solve \(t + 48=7t\).
Subtract \(t\) from both sides: \(48=7t - t\), so \(48 = 6t\).
Divide both sides by \(6\): \(t=\frac{48}{6}=8\).

Step3: Solve the equation for \(u\)

Solve \(u + 18=4u\).
Subtract \(u\) from both sides: \(18=4u - u\), so \(18 = 3u\).
Divide both sides by \(3\): \(u=\frac{18}{3}=6\).

Answer:

\(t = 8\), \(u = 6\)