Question

The lengths of the diagonals of a rhombus are 24 cm and 10 cm. Find each side of the rhombus.

Answer 1

We know that a quadrilateral is said to a rhombus if all sides of the quadrilateral are equal. Diagonals of a rhombus bisect each other at right angles.

Quadrilateral ABCD is a rhombus and diagonals AC and BD intersect at point O.

As we defined above, we get , , and angle .

We are given that AC = 10 cm and BD = 24 cm.

Therefore, we get, AO = OC = 5 cm and BO = OD = 12 cm.

Now we will use Pythagoras theorem in the right angled triangle AOD as below,

…......(1)

Now we will substitute the values of AO and OD in equation (1) we get,

Let us take the square root

AD = 13

Therefore, length of the side of the rhombus is .