Given that the area of a rhombus is 480 cm² and one of its diagonals is 48 cm, we need to find the following:

1. Length of the Other Diagonal

The area $A$ of a rhombus can be calculated using the formula: $A = \frac{1}{2} \times d_1 \times d_2$ where $d_1$ and $d_2$ are the lengths of the diagonals.

We know: $480 = \frac{1}{2} \times 48 \times d_2$

To find $d_2$: $d_2 = \frac{2 \times 480}{48} = \frac{960}{48} = 20 \text{ cm}$

2. Length of Each Side

The length of a side $s$ of the rhombus can be calculated using the relationship between the diagonals and the sides: $s = \sqrt{\left(\frac{d_1}{2}\right)^2 + \left(\frac{d_2}{2}\right)^2}$ Substituting the values $d_1 = 48$ cm and $d_2 = 20$ cm: $s = \sqrt{\left(\frac{48}{2}\right)^2 + \left(\frac{20}{2}\right)^2} = \sqrt{24^2 + 10^2} = \sqrt{576 + 100} = \sqrt{676} = 26 \text{ cm}$

3. Perimeter of the Rhombus

The perimeter $P$ of a rhombus is given by: $P = 4 \times s$ So, substituting the value of $s = 26$ cm: $P = 4 \times 26 = 104 \text{ cm}$

4. Distance Between Its Sides

The distance between the sides (also known as the height $h$) can be found using the area formula for the rhombus: $A = s \times h$ Rearranging to find $h$: $h = \frac{A}{s} = \frac{480}{26} \approx 18.46 \text{ cm}$

Summary of Results

1. Length of the other diagonal $d_2 = 20$ cm.
2. Length of each side $s = 26$ cm.
3. Perimeter of the rhombus $P = 104$ cm.
4. Distance between the sides (height) $h \approx 18.46$ cm.

Would you like any more details, or do you have any questions?

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Here are 5 related questions to further your understanding:

1. How would the area change if the other diagonal was doubled?
2. What is the relationship between the diagonals and the area of a rhombus?
3. How does the perimeter of a rhombus compare to its diagonals?
4. What are the properties of a rhombus that distinguish it from other quadrilaterals?
5. How would you find the area if both diagonals were unknown?

Tip: Remember that the diagonals of a rhombus bisect each other at right angles, forming four right-angled triangles within the rhombus.