how do you do this rhombus question??? find the length of the sides?

Question

If the diagonals of a rhombus have lengths of 12cm and 16 cm, what is the length in centimeters of one side of the rhombus?

Answer 1

Let ABCD be the rhombus. AC & BD be the diagonals of the rhombus.Let them intersect each other at O.We know that diagonals of a rhombus bisect each other other at right angles.Therefore half of the diagonals is equal to 6cm and 8cm. In right triangle OAB. OB^2 +OA^2=AB^2 (USING PYTHAGORAS THEOREM)
therefore 6^2 + 8^2=AB^2
or 36+64=AB^2
100=AB^2
10=AB

Therefore one side of the rhombus equals to 10 cm