Triangle ABC is shown. DE is a straight line with D on AC and E on BC AB = 46m, EC = 18m, CD = 29m and ED = 20m. Calculate the length AD.

37.7m

Step-by-step explanation:

Triangle ABC is shown. DE is a straight line with D on AC and E on BC AB = 46m, EC = 18m, CD = 29m and ED = 20m. Calculate the length AD.

We solve using Similarity Theorem

BA/AC =BD/DC

46/AD+29 = 20/29

Cross Multiply

46 × 29 =20 (AD + 29)

1334 = 20AD + 580

20AD = 1334 - 580

20AD = 754

AD = 754/20

AD = 37.7m

let's call the solutions x₁ = (5 - 2√7)/3 and x₂ = (5 + 2√7)/3

then the equation is (x-x₁)(x-x₂) = 0

if you fill that in you get a lot of numbers which you can recognize as ax²+bx+c=0.

step-by-step explanation:

you can see that a=1 (there is just an x²)

b = (-5 -2√7 + 2√7 - 5)/3 = -10/3

c = -2√7)/3 ) * (-5+2√7)/3) = -1/3

so your answer is 3x^2 – 10x – 1 = 0