How do you find the perimeter of a rhombus when its diagonals are 10 cm and 24 cm?

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To find the perimeter of a rhombus when you know the lengths of the diagonals, you can use the following steps:

  1. Determine the Lengths of the Diagonals: In this case, the lengths of the diagonals are given as 10 cm and 24 cm.
  2. Find the Length of One Side: The diagonals of a rhombus bisect each other at right angles. Thus, each half of the diagonals forms a right triangle with half-lengths of the diagonals as its two legs.
  3. Calculate half-lengths:
    • Half of the first diagonal: 10 cm / 2 = 5 cm
    • Half of the second diagonal: 24 cm / 2 = 12 cm
  4. Using the Pythagorean theorem to find the side length (s) of the rhombus:
    5. s = √(5² + 12²)
  5. Calculating it out: 
    6. s = √(25 + 144) = √169 = 13 cm
  6. Calculate the Perimeter: The perimeter (P) of a rhombus is calculated by the formula P = 4s.
    7. P = 4 × 13 = 52 cm

Therefore, the perimeter of the rhombus is 52 cm.

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