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The Diagonals Of A Rhombus Are 12 Cm And 16 Cm: A Comprehensive Guide

Mei 03, 2024 Posting Komentar

The length of the diagonal of a rhombus are 16cm & 12cm. find the side from brainly.in

If you're reading this article, chances are you're either a student trying to understand the concept of a rhombus or a curious individual who wants to know more about this geometric shape. In this article, we'll explore the diagonals of a rhombus and their properties, and how they relate to the shape as a whole.

What is a Rhombus?

A rhombus is a quadrilateral with four sides of equal length. It is also known as a diamond, as it resembles the shape of a diamond. A rhombus has two pairs of parallel sides and diagonals that bisect each other at right angles.

One of the defining characteristics of a rhombus is that its diagonals are perpendicular bisectors of each other. This means that the diagonals divide the rhombus into four congruent right triangles. Another important property of a rhombus is that its diagonals bisect the angles formed by its sides.

Properties of the Diagonals of a Rhombus

Now that we have a basic understanding of what a rhombus is, let's dive deeper into the diagonals of a rhombus. In this section, we'll explore their properties and how they relate to the shape as a whole.

Length of Diagonals

In a rhombus, the length of the diagonals is not equal. However, the product of the diagonals is always the same. This means that if we know the length of one diagonal, we can easily find the length of the other diagonal.

In our case, we know that the length of one diagonal is 12 cm and the length of the other diagonal is 16 cm. To find the product of the diagonals, we simply multiply them together:

Product of diagonals = 12 cm x 16 cm = 192 cm²

So, the product of the diagonals of our rhombus is 192 cm².

Relationship between Diagonals and Area

The diagonals of a rhombus are also related to its area. The area of a rhombus can be found by multiplying the length of its diagonals and dividing the product by two:

Area of rhombus = (12 cm x 16 cm) / 2 = 96 cm²

So, the area of our rhombus is 96 cm².

Relationship between Diagonals and Perimeter

The diagonals of a rhombus are also related to its perimeter. The perimeter of a rhombus can be found by multiplying the length of one of its sides by four:

Perimeter of rhombus = 4 x side length

Since all sides of a rhombus are equal, we can also find its perimeter by multiplying the length of one side by four:

Perimeter of rhombus = 4 x side length = 4 x 10 cm = 40 cm

So, the perimeter of our rhombus is 40 cm.

Using the Diagonals to Find the Side Lengths

Now that we know the length of the diagonals and the area of our rhombus, we can use this information to find the length of its sides.

First, we need to find the length of one of the diagonals. We know that the product of the diagonals is 192 cm², and we also know that one of the diagonals is 12 cm. To find the length of the other diagonal, we divide the product by the length of the known diagonal:

Length of other diagonal = 192 cm² / 12 cm = 16 cm

So, the length of the other diagonal is 16 cm.

Next, we can use the length of the diagonals and the area of the rhombus to find the length of its sides. The formula for finding the length of the sides of a rhombus is:

Side length = (2 x area) / (diagonal 1 + diagonal 2)

Substituting in the values we know:

Side length = (2 x 96 cm²) / (12 cm + 16 cm) = 48 cm / 28 cm
Side length = 1.71 cm

So, the length of each side of our rhombus is 1.71 cm.

Conclusion

In conclusion, we've explored the diagonals of a rhombus and their properties. We've learned that the diagonals of a rhombus are perpendicular bisectors of each other, and that they bisect the angles formed by its sides. We've also learned that the length of the diagonals is not equal, but that the product of the diagonals is always the same. We've seen how the diagonals are related to the area and perimeter of a rhombus, and how they can be used to find the length of its sides. Hopefully, this article has helped you to better understand the concept of a rhombus and its diagonals.

Remember: The diagonals of a rhombus are key to understanding its properties and can be used to find the length of its sides. Knowing the length of the diagonals can also help you find the area and perimeter of a rhombus. Keep these properties in mind when working with rhombuses in the future!