Question

If z is the midpoint of SU, what are ST, TU, and SU?a. ST = 8, TU = 40, and SU = 80b. ST = 10, TU = 10, and SU = 20c. ST = 54, TU = 54, and SU = 108d. ST = 40, TU = 40, and SU = 80

Answer 1

If T is the midpoint, then, it is necessary that ST = TU. Use the given expressions for ST and TU:

ST = 9x

TU = 6x + 30

equal the previous expressions and solve for x, as follow:

ST = TU

9x = 6x + 30 subtract 6x both sides

9x - 6x = 30 simplify left side

3x = 30 divide by 3 both sides

x = 30/3

x = 10

next, replace the value of x into the expressions for ST and TU:

ST = 9x = 9(10) = 90

TU = 6x + 30 = 6(10) + 30 = 60 + 30 = 90

and the value of SU is:

SU = ST + TU = 90 + 90 = 180

Then, you have:

ST = 90, TU = 90, SU = 180