The diagonals of the rhombus are 10cm and 24cm, what is the side of the rhombus?

The intersection point of the diagonals in the rhombus divides the diagonals in half. The diagonals in the rhombus are perpendicular to each other, therefore, they form 4 identical right-angled triangles in the rhombus, in which the side of the rhombus is the hypotenuse. Find the half-diagonal of the rhombus:

10/2 = 5 cm – the first leg of a right-angled triangle;

24/2 = 12 cm – the second leg of the right triangle.

Now we will find the hypotenuse of a right-angled triangle by the Pythagorean theorem. This will be the side of the diamond.

a² + b² = c²;

5² + 12² = c²;

25 + 144 = c²;

c² = 169;

c = 13 cm – rhombus side.

Answer: 13 cm