Question

Given ΔQRS≅ΔTUV, QS=3v+2andTV=7v−6, find the length of QS and TV.

Answer 1

Since the triangles ΔQRS and ΔTUV, their corresponding sides are also congruent, this means that

`\begin{gathered} QR\cong TU \\ RS\cong UV \\ QS\cong TV \end{gathered}`

Since QS and TV are congruent, this means that they have the same measures, therefore

`\begin{gathered} QS=TV \\ 3v+2=7v-6 \end{gathered}`

Solving this equation for v, we have

`\begin{gathered} 3v+2=7v-6 \\ 3v-7v+2=-6 \\ -4v=-6-2 \\ 4v=8 \\ v=2 \end{gathered}`

Using this value for v in our expression for the sides, we have

`\begin{gathered} QS=3\cdot2+2=8 \\ TV=7\cdot2-6=8 \end{gathered}`

Both sides are equal to 8.