Option C:
The value of x is 8.
Solution:
Given MNOP is a trapezoid.
QR is the mid-segment of the trapezoid.
NO = 4x – 16, MP = 32, QR = x + 16
The mid-segment of a trapezoid is half the of the sum of the two parallel sides.
[tex]$QR=\frac{1}{2}(NO+MP)[/tex]
[tex]$x+16=\frac{1}{2}(4x-16+32)[/tex]
[tex]$x+16=\frac{1}{2}(4x+16)[/tex]
Do cross multiplication.
[tex]2(x+16)=(4x+16)[/tex]
[tex]2x+32=4x+16[/tex]
Subtract 16 on both sides.
[tex]2x+16=4x[/tex]
Subtract 2x on both sides of the equation.
[tex]16=2x[/tex]
Divide by 2 on both sides of the equation.
8 = x
x = 8
Option C is the correct answer.
Hence the value of x is 8.
