Question

Give Triangle QRS ~= Triangle TUV, QS = 3v + 2 and TV = 7v - 6, find the length of QS and TV

Answer 1

$QS\cong TV=8$

1) Since these triangles are congruent, then we can write out the following for congruent triangles have congruent sides:

$\begin{gathered} QS=TV \\ 3v+2=7v-6 \\ 3v-7v=-6-2 \\ -4v=-8 \\ 4v=8 \\ \frac{4v}{4}=\frac{8}{4} \\ v=2 \end{gathered}$

2) Still based on that principle, we can plug v=2 into any of those formulas to get the measure of QS and TV. So let's pick the simpler one:

$\begin{gathered} QS=3v+2 \\ QS=3(2)+2 \\ QS=6+2 \\ QS=8 \\ --- \\ TV=7(2)-6 \\ TV=14-6 \\ TV=8 \end{gathered}$

As we can see these segments are congruent.