Question

Construct a square ABCD whose one diagonal BD = 5.6 cm.

Answer 1

Given: Square ABCD with diagonal BD = 5.6 cm.

Step-wise calculation:

1. In a square, the diagonal d and side s satisfy `d = sqrt(2)`.

2. Therefore, `s = d/sqrt(2)`

= `5.6/sqrt(2)`

= `2.8sqrt(2)`

= 3.959... ≈ 3.96 cm

3. Half the diagonal

= `(BD)/2`

= `5.6/2`

= 2.8 cm

This is the distance from the intersection point of the diagonals midpoint O to each vertex.

Construction steps (straightedge and compass):

1. Draw BD of length 5.6 cm.
2. Construct the perpendicular bisector of BD to locate its midpoint O. Use arcs from B and D and join their intersections. This line is the other diagonal AC.
3. With O as centre and radius 2.8 cm, half the diagonal, mark the two points where this radius meets the perpendicular bisector; label them A and C, one on each side of BD.
4. Join A to B, B to C, C to D and D to A.