Answer:
CE = 35
Step-by-step explanation:
Δ CBD and Δ CAE are similar thus ratios of corresponding sides are equal, that is
[tex]\frac{CB}{CA}[/tex] = [tex]\frac{CD}{CE}[/tex] , substitute values
[tex]\frac{x-5}{x-5+6}[/tex] = [tex]\frac{14}{14+2x + 3}[/tex] , then
[tex]\frac{x-5}{x+1}[/tex] = [tex]\frac{14}{2x +17}[/tex] ( cross- multiply )
(x - 5)(2x + 17) = 14(x + 1) ← distribute both sides
2x² + 7x - 85 = 14x + 14 ( subtract 14x + 14 from both sides )
2x² - 7x - 99 = 0 ← in standard form
(x - 9)(2x + 11) = 0 ← in factored form
quate each factor to zero and solve for x
x - 9 = 0 ⇒ x = 9
2x + 11 = 0 ⇒ 2x = - 11 ⇒ x = - [tex]\frac{11}{2}[/tex]
but x > 0 , thus x = 9
Hence
CE = 2x + 17 = 2(9) + 17 = 18 + 17 = 35
