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

step-by-step explanation:

two pairs of adjacent sides are of equal length. this implies that one diagonal divides the kite into congruent triangles, and so the angles between the two pairs of equal sides are equal in measure. it also implies that the diagonals are perpendicular.