Rectangle abcd and right triangle dce have the same area. they are joined to form a trapezoid, as shown. what is de?

Since the areas are the same  (5 x 6 = 30 units), and the height of the triangle (DC) is 5 so the length of the triangle must be 12.  (1/2 of  5 x 12 is also 30)

So now we use the Pythagorean theorem

a² + b² = c²   we have 5² + 12² = c²  or 25 + 144 = c²  or 169 = c²

The square root of 169 is 13 so side DE is 13 units.

Best answer that i found on yahoo ok   set :   x= length of 2nd piece in cm  x- 3= length of 1st piece in cm  x-4= length of 3rd piece in cm  then since you know they all came from the 20 cm ribbon you add them together and set them equal to 20x+ x-3 +x-4 = 20  3x - 7= 20  3x= 27  x= 9  the shortest piece is the third piece which is x- 4  x-4  9-4 = 5  the length of the smallest piece is 5 cm.  the other lengths are  9 cm  6 cm