Answer:
CE = 35
Step-by-step explanation:
Based on the Triangle Proportionality Theorem, BD divides AC and CE proportionally. This implies that:
BC:AB = DC:DE
Plug in the values
(x - 5)/6 = 14/(2x + 3)
(x - 5)(2x + 3) = 14*6
x(2x + 3) -5(2x + 3) = 84
2x² + 3x - 10x - 15 = 84
2x² - 7x - 15 - 84 = 0
2x² - 7x - 99 = 0
Factorize
2x² - 18x + 11x - 99 = 0
2x(x - 9) +11(x - 9) = 0
(2x + 11)(x - 9) = 0
2x = -11
x = -11/2
Or
x = 9
Let's take the positive value of x
Thus:
CE = 14 + 2x + 3
Plug in the value of x
CE = 14 + 2(9) + 3
CE = 14 + 18 + 3
CE = 35
