Two sides of a triangle have lengths 18m and 23m. describe the possible lengths of the third side.

The possible length of third side is between 5 and 41 m

Step-by-step explanation:

Given two sides of a triangle have lengths 18 m and 23 m.

we have to describe the possible lengths of the third side.

The triangle holds the inequality which states that, the third side must have a length between the sum and difference of the other two sides i.e

If a, b, c are the sides of triangle then

a-b<c<a+b

Here the two sides which are given

18 m and 23 m

23 - 18  < third side < 18 + 23

5  < third side < 41

The possible length of third side is between 5 and 41 m

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