Given that qrvtsu is a regular hexagon what are the lengths of qr and st?

Option A. 37

Step-by-step explanation:

We will understand first what is a regular hexagon?

Hexagon is a structure in which number of all the sides are 6 and since its a regular hexagon all the sides will be equal.

Since all the sides are equal and given two sides are (3y + 19) and (6y + 1)

Therefore, by the definition of regular hexagon

3y + 19 = 6y + 1

19 = 6y - 3y + 1

19 - 1 = 6y - 3y

18 = 3y

y =

Now we have to calculate the length of both the sides given.

Side ST = 6y + 1 = 6×6 + 1 = 36 + 1 = 37

and QR = 3y + 19 = 3×6 + 19 = 18 + 19 = 37

Therefore, option A. 37 is the correct answer.

see explanation

Step-by-step explanation:

Solving each equation

x + 6 = 2 ( subtract 6 from both sides )

x = - 4 ≠ 8

x + 2 = 10 ( subtract 2 from each side )

x = 8 ← True

x - 4 = 4 ( add 4 to both sides )

x = 8 ← True

x - 2 = 10 ( add 2 to both sides )

x = 12 ≠ 8

2x = 4 ( divide both sides by 2 )

x = 2 ≠ 8

3x = 24 ( divide both sides by 3 )

x = 8 ← True

The equations where x is a solution are

x + 2 = 10 , x - 4 = 4 and 3x = 24