Question

Construct a rhombus ABCD, when AC = 6 cm and BD = 8 cm. Measure AB.

Answer 1

Given:

Rhombus ABCD with diagonals AC = 6 cm and BD = 8 cm.

Stepwise calculation:

1. Recall the property of rhombus its diagonals bisect each other at right angles.

2. Let O be the midpoint of both diagonals AC and BD.

`AO = OC = (AC)/2 = 6/2 = 3` cm

`BO = OD = (BD)/2 = 8/2 = 4` cm

3. Triangle ABO is a right triangle because diagonals intersect at right angles with sides AO = 3 cm and BO = 4 cm.

4. Use Pythagoras theorem to find AB:

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

= `sqrt(3^2 + 4^2)`

= `sqrt(9 + 16)`

= `sqrt(25)`

= 5 cm

The length of side AB of the rhombus is 5 cm.