Question

Construct a rectangle ABCD in which AB = 6 cm and BC = 4.8 cm.

Answer 1

Given: Rectangle ABCD with AB = 6 cm and BC = 4.8 cm.

Step-wise construction (compass and straightedge):

1. Draw the base AB of length 6 cm using a ruler; mark endpoints A and B.
2. Through B construct a line perpendicular to AB. Erect the perpendicular at B using your usual compass-and-straightedge method or a set square.
3. On that perpendicular, from B mark point C so that BC = 4.8 cm.
4. With center A and radius 4.8 cm, draw an arc. With center C and radius 6 cm, draw another arc. Let the two arcs intersect at D. These radii ensure AD = BC and CD = AB.
5. Join A to D and C to D to complete the quadrilateral ABCD.

Verification:

AD was drawn with radius 4.8 from A, so AD = BC = 4.8 cm.

CD was drawn with radius 6 from C, so CD = AB = 6 cm.

AB and BC are adjacent and the line through B was constructed perpendicular to AB, so angle ABC = 90°. Because AD is parallel to BC equal length and constructed from A with the same offset and CD is parallel to AB, all angles are right angles. 

Therefore, all four angles are 90° and opposite sides are equal, so ABCD is a rectangle.

The figure ABCD constructed as above satisfies AB = 6 cm, BC = 4.8 cm and has four right angles; hence ABCD is the required rectangle.