The area of a rhombus is given as 384 cm², and its

Solution

Length of each side of the rhombus = 80 ÷ 4 = 20 cm

Let the length of longer diagonal be '2x' cm and that of smaller diagonal be '2y' cm.

So, (1/2) X 2x X 2y = 384

Or, xy = 192

Now, since the diagonals of a rhombus are perpendicular bisectors of each other. So, ABC is a right angled triangle.

And, in triangle ABC, we have

x² + y² = 400

Since, (x + y)² = x² + y² + 2xy

So, (x + y)² = 400 + 2 X 192

Or, (x + y)² = 784

So, x + y = 28

So, required sum = 28 X 2 = 56 cm