The perimeter of a rectangle is twice the sum
of its length and its width. the perimeter is
40 meters and its length is 2 meters more
than twice its width.

The width of the given rectangle  =  6 m

The width of the rectangle  = 14 m

Step-by-step explanation:

Let us assume the width of the rectangle  = k

So, the length of the rectangle  =  2 + 2 ( The width)  = 2 +  2 k

Perimeter of the rectangle  = 40 meters

Now, PERIMETER OF THE RECTANGLE = 2(LENGTH + WIDTH)

or, 40 =  2 ( k + (2 +  2 k))

⇒ 2( 3  k + 2) = 40

or, 2(3 k) +  2(2) = 40

or, 6 k = 40 - 4  =  36

⇒ k = 36 / 6 = 6, or  k = 6

Hence, the width of the given rectangle  = k = 6 m

The width of the rectangle = 2 + 2 k =  2 + 2(6)  = 14 m