Triangle DEF is similar to triangle ABC. What is the length of segment EF? (HINT use scale factor) (Leave answer as a fraction)

We have been given two similar triangles. We are asked to find the length of segment EF.

We know that corresponding sides of similar triangles are proportional, so we will use proportion to solve our given problem.

Upon substituting measure of our given side lengths, we will get:

Therefore, the length of segment EF is units.

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