To find the perimeter of the rhombus, we can use the fact that the diagonals of a rhombus bisect each other at right angles. Given that the diagonals are 6 m and 8 m, we can treat each half of these diagonals as the legs of a right triangle, with the side of the rhombus as the hypotenuse.

Step-by-Step Solution:

1. The diagonals are 6 m and 8 m, so each half of the diagonals will be: $\frac{6}{2} = 3 \text{ m} \quad \text{and} \quad \frac{8}{2} = 4 \text{ m}$

2. Each side of the rhombus forms the hypotenuse of a right triangle with legs of 3 m and 4 m. Using the Pythagorean theorem: $s = \sqrt{3^2 + 4^2} = \sqrt{9 + 16} = \sqrt{25} = 5 \text{ m}$

3. Since all four sides of a rhombus are equal, the perimeter $P$ is: $P = 4 \times s = 4 \times 5 = 20 \text{ m}$

Answer:

The perimeter of the rhombus is 20 meters.

Would you like a detailed breakdown of any specific step or have any questions?

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Here are some related questions you might explore:

1. How would you find the area of the same rhombus?
2. What properties of a rhombus help determine its perimeter?
3. Can you find the length of the sides of a rhombus if only one diagonal and the perimeter are known?
4. How does the Pythagorean theorem apply to other quadrilaterals?
5. If the diagonals of a rhombus were 10 m and 24 m, what would be its perimeter?

Tip: Remember, in a rhombus, diagonals always bisect each other at right angles, creating right triangles for calculations.