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

Question

3 years ago

8

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

Mathematics

2 answers:

Andre45 [30] · Answer 1 · 2022-04-10T17:15:55+03:00

Andre45 [30]3 years ago

9 0

Answer:

25

Step-by-step explanation:

alexandr1967 [171] · Answer 2 · 2022-04-10T15:54:26+03:00

Answer:

$RS=25\ units$

Step-by-step 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

$RS=25\ units$