The lengths of the sides of a quadrilateral are 4 consecutive even integers. The perimeter of the quadrilateral is 36 inches. What is the length of the longest side?

12 inches

Step-by-step explanation:

Even integers are multiple of 2 and differ by 2.

Thus,

as quadrilaterals have 4 sides

let the length of those sides be

2x , 2x + 2 , 2x+4, 2x+6

given that their sum is 36 inches

thus

lets take sum of assumed sides

2x + 2x + 2 + 2x+4 +  2x+6 = 36

=> 8x + 12 = 36

=> 8x = 36 - 12 = 24

=> x = 24/8 = 3

Thus,

sides are

2x = 2*3 = 6

2x + 2 = 6 +2 = 8

2x + 4 = 6 + 4 = 10

2x + 6 = 6 + 6 = 12

Thus,

length of longest side is 12 inches.

it would open into a square depending on the type of envelope i’m not sure about the second part