Question

Plz Help!!! Given triangle QRS is congruent to triangle TUV, QS equals 3v +2 and TV equals 7v-6, find the length of QS and TV

ありがと！！！ Thank you!

Answer 1

8

Explanation:

Two triangles are congruent if their corresponding sides are equal in length, and their corresponding angles are equal in measure. Having this in mind:

`QS=TV`

Where:

`QS=3v+2\\TV=7v-6`

So, we will have the next equation:

`3v+2=7v-6`

Solving for v:

Subtract 3v from both sides:

`3v-3v+2=7v-6-3v\\2=4v-6`

Add 6 to both sides:

`6+2=4v-6+6\\8=4v`

Divide both sides by 4:

`(8)/(4) =(4)/(4)v\\ 2=v`

Finally, replacing the value of v in QS and TV:

`QS=3(2)+2=6+2=8\\TV=7(2)-6=14-6=8`

どういたしまして!