contestada

In the diagram, the length of segment VS is 39 units.

Line n is a perpendicular bisector of line segment T V. It intersects line segment T V at point R. Line n also contains points Q and S. Line segment Q V is 3 x + 4. Line segment R V is 2 x + 5. Line segment T S is 6 x minus 3.
What is the length of segment TV?

14 units
19 units
38 units
50 units

Respuesta :

luisejr77

Answer: THIRD OPTION.

Step-by-step explanation:

The missing figure is attached.

You can observe in the figure two equal right triangles: RST and RSV.

Notice that:

[tex]TS=VS[/tex]

Knowing that:

 [tex]TS=6x-3\\\\VS=39[/tex]

You can substitute values into the equation and solve for "x":

 [tex]6x-3=39\\\\6x=39+3\\\\6x=42\\\\x=\frac{42}{6}\\\\x=7[/tex]

Now, you can identify in the figure that:

[tex]RV=2x+5[/tex]

Having the value of "x" calculated above, you can subsitute into the equation and evaluate, in order to find the length of segment RV:

[tex]RV=2(7)+5\\\\RV=14+5\\\\RV=19\ units[/tex]

Since:

[tex]RV=RT[/tex]

You get that:

[tex]RT=19\ units[/tex]

Finally, you must add RT and RV in order to find the length of the segment TV. This is:

[tex]TV=19\ units+19\ units\\\\TV=38\ units[/tex]

Ver imagen luisejr77

Answer:

38 units

Step-by-step explanation:

yes

Otras preguntas