The diagonal of the rhombus is 24cm, its perimeter is 52cm. Calculate the length of the second diagonal.

All sides of the rhombus are equal, so one side is equal to:

a = P / 4, where P is the perimeter of the rhombus.

Find the side of the rhombus:

a = 52/4 = 13 cm.

The side of the rhombus and the halves of its diagonals form right-angled triangles between themselves, where the side of the rhombus is its hypotenuse. By the Pythagorean theorem:

a² = b² + c², where b and c are the legs of the triangle.

Find b:

b = 24/2 = 12 cm.

Let’s substitute their values ​​instead of a and b and solve the resulting equation:

12² + c² = 13²,

144 + c² = 169,

c² = 169 – 144,

c² = 25,

c = √25,

c = 5 cm.

We found half of the second diagonal. Let’s find its full length:

5 * 2 = 10 cm.

Answer: the length of the second diagonal of the rhombus is 10 cm.