Question

Please Help! :( Segment TQ is 26 units long. What is the length of QV? 8 units 26 units 31 units 32 units

Answer 1

31

Explanation:

Answer 2

The length of QV is 31 units

Explanation

Notice that triangle STR and triangle TQR are congruent by Side-Angle-Side, so ST = TQ

We also know that TQ = 26, and we can infer from our diagram that
`ST = 3x+2`, so let's replace the values:

ST = TQ

`3x+2=26`

`3x=24`

`x=(24)/(3)`

`x=8`

Also, notice that triangle SVR is congruent to Triangle VQR by Side-Angle-Side as well, so QV = SV

We know that
`SV=4x-1`, so let's replace the value:

`QV=4x-1`

Since we know that
`x=8`, we can replace the value to find QV:

`QV=4x-1`

`QV=4(8)-1`

`QV=32-1`

`QV=31`