Question

If I is the midpoint of SU, what are ST, TU, and SU?

S. T. U
5x 3x + 24
A. ST = 60. TU = 60. and SU = 120
B. ST = 78. TU = 78. and SU = 156
C. ST = 15, TU = 15, and SU = 30
D. ST = 12, TU = 60, and SU = 120

Answer 1

SI and IU are equal, and with segments ST and TU being parts of these and given as 5x and 3x + 24 respectively, we find x to be 12. This makes ST = 60, TU = 60, and SU = 120.

Step-by-step explanation:

If I is the midpoint of SU, then SI and IU are equal in length. Thus, for the segments ST and TU, which are parts of SI and IU respectively, we have been given the expressions 5x for ST and 3x + 24 for TU. Since SI = IU, we can set 5x equal to 3x + 24 to find the value of x.

Solving the equation:

• 5x = 3x + 24
• 2x = 24
• x = 12

Plugging x back in:

• ST = 5(12) = 60
• TU = 3(12) + 24 = 60
• Since ST = TU, and both are half of SU, then SU = 60 + 60 = 120

Therefore, the correct answer is ST = 60, TU = 60, and SU = 120 (Answer A).