If the diagonal of a rhombus is 10 and 24 what will be it's perimeter

The diagonal of a rhombus divides it into four right-angled triangles. Given the diagonals of a rhombus, we can find the side length using the Pythagorean theorem.

Let's denote the diagonals as \(d_1 = 10\) and \(d_2 = 24\).

Since the diagonals bisect each other at right angles, each side of the rhombus is the hypotenuse of a right triangle with legs \(\frac{d_1}{2} = 5\) and \(\frac{d_2}{2} = 12\).

Using the Pythagorean theorem, we can find the side length \(s\) of the rhombus:

\[ s = \sqrt{\left(\frac{d_1}{2}\right)^2 + \left(\frac{d_2}{2}\right)^2} \]
\[ s = \sqrt{5^2 + 12^2} \]
\[ s = \sqrt{25 + 144} \]
\[ s = \sqrt{169} \]
\[ s = 13 \]

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

\[ P = 4 \times s \]
\[ P = 4 \times 13 \]
\[ P = 52 \]

Therefore, the perimeter of the rhombus is \(52\).

Would you like more details or have any questions?

Here are some related questions you might find interesting:

1. How do you calculate the area of a rhombus given its diagonals?
2. What are the properties of the diagonals in a rhombus?
3. How does the Pythagorean theorem apply to the geometry of a rhombus?
4. Can you prove that the diagonals of a rhombus bisect each other at right angles?
5. How do you find the side length of a rhombus given its perimeter?
6. What is the relationship between the side length and the diagonals in a rhombus?
7. How do you calculate the perimeter of a rhombus if only one diagonal and one side are given?
8. How does the area of a rhombus compare to the area of a rectangle with the same diagonals?

**Tip:** In geometry, visualizing shapes and their properties can greatly aid in understanding and solving problems.

Learn how to calculate the perimeter of a rhombus with diagonals 10 and 24. This problem involves using the Pythagorean theorem to find the side length of the rhombus, followed by calculating its perimeter. Suitable for students in Grades 7-9 studying geometry.

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