If Z is the midpoint of modifying above R T with bar, what are x, RZ, and RT?
Line segment RT is shown. Its midpoint is labeled Z. Segment RZ has a length of 4 x minus 28 and segment ZT has a length of 24.
(1 point)
Responses
x = 13, RZ = 48, and RT = 24
x = 13, RZ = 48, and RT = 24
x = 11, RZ = 16, and RT = 32
x = 11, RZ = 16, and RT = 32
x = 13, RZ = 24, and RT = 48
x = 13, RZ = 24, and RT = 48
x = 15, RZ = 24, and RT = 48
x = 13, RZ = 24, and RT = 48
To find the values of x, RZ, and RT, we can use the given information that the length of segment RZ is 4x - 28 and the length of segment ZT is 24. Since Z is the midpoint of segment RT, we know that the lengths of segments RZ and ZT are equal.
Setting up the equation:
4x - 28 = 24
Solving for x:
Add 28 to both sides:
4x = 52
Divide both sides by 4:
x = 13
Therefore, x = 13.
Using x = 13, we can find the values of RZ and RT.
Substituting x = 13 into the expression for RZ:
RZ = 4x - 28
RZ = 4(13) - 28
RZ = 52 - 28
RZ = 24
Therefore, RZ = 24.
Since Z is the midpoint, we know that the lengths of RZ and ZT are equal. We are given that ZT has a length of 24, so RT also has a length of 24.
Therefore, x = 13, RZ = 24, and RT = 24.