Question

In the diagram, TQ is 18 units in length. Line l is a perpendicular bisector of line segment R Q. It intersects line segment R Q at point T. Line l also contains point S. Line segment R T is 2 x + 10. Line segment S Q is 9 x minus 11. What is the length of RS? 16 units 18 units 25 units 46 units

Answer 1

25

Explanation:

Answer 2

`RS=25\ units`

Explanation:

we know that

If line I s a perpendicular bisector of line segment R Q at point T

then

T is the midpoint of line segment RQ

and

`RT=TQ`

we have

`TQ=18\ units`

so

`RT=18\ units`

Find the value of x

we have

`RT=2x+10`

substitute the value of RT

`18=2x+10`

solve for x

`2x=18-10\\2x=8\\x=4`

Find the value of SQ

`SQ=9x-11`

substitute the value of x

`SQ=9(4)-11=25\ units`

we have that

Triangle RTS and Triangle QTS are congruent by SAS

see the attached figure to better understand the problem

so

`RS=SQ`

therefore

`RS=25\ units`