Question

Construct a rhombus ABCD in which AC = 6.4 cm and BD = 8 cm.

Answer 1

Given:

AC = 6.4 cm

BD = 8 cm

Step-wise calculation:

In a rhombus, the diagonals bisect each other at right angles.

AO = OC

= `(AC)/2`

= `6.4/2`

= 3.2 cm

BO = OD

= `(BD)/2`

= `8/2`

= 4.0 cm

Step-wise construction:

1. Draw BD = 8.0 cm.
2. Construct the perpendicular bisector of BD to locate its midpoint O. Use compass arcs from B and D and join their intersection points. O is the intersection/midpoint, so BO = OD = 4.0 cm.
3. With O as centre and radius 3.2 cm, draw two arcs on opposite sides of BD; their intersections with the perpendicular bisector give points A and C so that AO = OC = 3.2 cm.
4. Join A to B, B to C, C to D and D to A.

ABCD is the required rhombus with AC = 6.4 cm and BD = 8.0 cm diagonals bisect at O with AO = OC = 3.2 cm and BO = OD = 4.0 cm.