A square has side length 6x+2. A rectangle with width 3x+1 has the same area as a square. What is the length of the rectangle

L = 12x + 4

Step-by-step explanation:

(see diagram for reference)

the area of the square

= (6x+2) (6x+2)  (factor out 2 from each parentheses)

= (2)(3x+1)(2)(3x+1)  (group like terms and simplify)

= 4(3x + 1)²

the area of the rectangle,

= (3x+1) (L)

It is given that the square and the circle have the same area, hence we equate the areas of square and rectangle:

4(3x + 1)² = (3x+1) (L)     (divide both sides by 3x+1)

4(3x + 1) = (L)   (rearranging and expanding the parentheses)

L = 12x + 4

Hope this helps

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