Answer:
CD = 15
x = 5
Step-by-step explanation:
Since BF ≅ FD and AE ≅ EC, then [tex]EF = \frac{AB + CD}{2}[/tex]
So, [tex]30 = \frac{x^{2} +20 + x^{2} + 22x - 120}{2}[/tex]
[tex]60 = 2x^{2} + 22x - 100[/tex]
[tex]2x^{2} + 22x - 160 = 0[/tex]
[tex]2(x^{2} + 11x - 80) = 0[/tex]
2(x - 5)(x + 16) = 0
x = 5 or x = -16
If x = 5, then CD = [tex]5^{2} +22(5) - 120 = 25 + 110 - 120 = 15[/tex]
Ix x = -16, then CD = will be a negative number which it cannot be.
