If diagonals of a rhombus is 10cm and 24cm, find its perimeter

To find the perimeter of a rhombus, we first need to determine the length of one of its sides. The diagonals of a rhombus bisect each other at right angles. In this case, the given diagonals are 10 cm and 24 cm.

Since the diagonals bisect each other, we can find the lengths of the halves:

• Half of the first diagonal = 10 cm / 2 = 5 cm
• Half of the second diagonal = 24 cm / 2 = 12 cm

Now, we can use the Pythagorean theorem to find the length of a side of the rhombus:

Side length (s) = √(5 cm² + 12 cm²)

Side length (s) = √(25 cm² + 144 cm²)

Side length (s) = √(169 cm²)

Side length (s) = 13 cm

The perimeter (P) of a rhombus is given by the formula:

P = 4 × side length

P = 4 × 13 cm = 52 cm

Thus, the perimeter of the rhombus is 52 cm.