construct a rhombus whose diagonals are 6cm , 8cm

It is quite simple!!

I am using a property of rhombus for drawing the figure.

"Diagonals of a rhombus are perpendicular bisectors of each other."

Draw a circle using compass having radius 4cm(8cm bisected)

With same centre draw another circle having radius 3cm(6cm bisected)

Now you have 2 concentric circles.

Now take radius=5cm [sqrt(4*4 + 3*3 )] Pythagorus theorem since the diagonals are perpendicular to each other and the radius being the hypotenuse.

Choose a point on the circle and draw a curve cutting the circle at 2 pts.

Draw the bigger diagonal (Length=8cm using this pt and centre)

Now place the pointer on the other end of the diagonal and draw another curve cutting the circle at 2 pts.

Just join the 2 intersections with the points on the outer circle.

You got it.