Question

Help please!! Find CE (parallel lines and proportional parts)

Answer 1

CE = 35

Explanation:

BD is parallel to AE and intersects the other 2 sides, dividing those sides proportionally, that is

`(14)/(2x+3)` =
`(x-5)/(6)` ( cross- multiply )

(x - 5)(2x + 3) = 84 ← expand left side using FOIL

2x² - 7x - 15 = 84 ( subtract 84 from both sides )

2x² - 7x - 99 = 0 ← in standard form

(2x + 11)(x - 9) = 0 ← in factored form

Equate each factor to zero and solve for x

x - 9 = 0 ⇒ x = 9

2x + 11 = 0 ⇒ 2x = - 11 ⇒ x = -
`(11)/(2)`

but x > 0 , thus x = 9

Then

CE = 14 + 2x + 3

= 17 + 2(9)

= 17 + 18

= 35