Answer:
ST = 15
Step-by-step explanation:
Given:
QR = 3x
LM = x + 9
ST = 6x - 3
Required:
ST
Solution:
First, we need to find the value of x by creating an equation.
Based on the trapezoid mid-segment theorem, we have the following equation:
LM = ½(QR + ST)
Substitute
x + 9 = ½(3x + 6x - 3)
x + 9 = ½(9x - 3)
Multiply both sides by 2
2(x + 9) = 9x - 3
2x + 18 = 9x - 3
Collect like terms
2x - 9x = -18 - 3
-7x = -21
Divide both sides by -7
x = -21/-7
x = 3
Find ST:
ST = 6x - 3
Plug in the value of x
ST = 6(3) - 3 = 18 - 3
ST = 15
