Question

Construct a rhombus ABCD, when AC = 12 cm and BD = 9 cm. Measure AB.

Answer 1

Given:

Rhombus ABCD with diagonals AC = 12 cm and BD = 9 cm.

Step wise calculation:

1. Recall the properties of a rhombus:

The diagonals bisect each other at right angles.

Each side of the rhombus can be found using the half-lengths of the diagonals, as the diagonals form right triangles with the sides.

2. Let O be the intersection point of diagonals AC and BD.

Then `AO = OC = (AC)/2 = 12/2 = 6` cm

`BO = OD = (BD)/2 = 9/2 = 4.5` cm

3. Triangle AOB is a right triangle with AO and BO as legs.

The side AB is the hypotenuse.

Using Pythagoras theorem:

`AB = sqrt((AO)^2 + (BO)^2)`

= `sqrt(6^2 + 4.5^2)`

= `sqrt(36 + 20.25)`

= `sqrt(56.25)`

= 7.5 cm

The length of side AB of the rhombus is 7.5 cm.