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A rhombus has diagnosed of length 8 cm and 10 cm find its perimeter

User Serket
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The perimeter of the given rhombus, with diagonals of 8 cm and 10 cm, is 25.61 cm. This is determined by finding the side length using the Pythagorean theorem and then multiplying it by 4.

To determine the perimeter of a rhombus, recognize that all its sides are of equal length. Given diagonals of 8 cm and 10 cm, designate the length of each side as "s."

The diagonals bisect each other at right angles, creating four congruent right-angled triangles. Applying the Pythagorean theorem, the side length can be found:

s = √((d₁/2)² + (d₂/2)²)

For this rhombus:

s = √((8/2)² + (10/2)²)

s = √(16 + 25)

s = √41

Thus, each side measures √41 cm.

The perimeter (P) of a rhombus is four times the side length:

P = 4s

P = 4 × √41

P = 25.61

Therefore, the perimeter of the rhombus is 25.61 cm.

User Sameera Lakshitha
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