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

Answer:

31

Step-by-step explanation:

Answer 2

Answer

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

$3x+2=26$

$3x=24$

$x=\frac{24}{3}$

$x=8$

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:

$QV=4x-1$

$QV=4(8)-1$

$QV=32-1$

$QV=31$