The Length Of Diagonals Of A Rhombus Are 16 And 12

Maret 25, 2024 Posting Komentar

MCQ The lengths of the diagonals of a rhombus are 16 cm and 12 cm from www.teachoo.com

Are you wondering about the length of diagonals of a rhombus? If yes, then you are in the right place. In this article, we will discuss the length of diagonals of a rhombus that are 16 and 12. Rhombus is a four-sided figure in which all sides are equal in length. The opposite sides of the rhombus are parallel to each other, and the diagonals bisect each other at right angles.

What is a Rhombus?

A rhombus is a type of quadrilateral in which all four sides are equal in length. It has two pairs of parallel sides, and the opposite angles are equal. The diagonals of a rhombus bisect each other at right angles, and their lengths are not equal. The length of the diagonals of a rhombus can be calculated using the Pythagorean theorem.

How to Calculate the Length of Diagonals of a Rhombus?

Let us consider a rhombus ABCD in which AC and BD are the diagonals of the rhombus. The length of the diagonals of the rhombus can be calculated using the Pythagorean theorem. The Pythagorean theorem states that the square of the hypotenuse is equal to the sum of the squares of the other two sides.

So, in the rhombus ABCD, we can say that:

AC² = AB² + BC²
BD² = AB² + AD²

As we know that the length of the diagonals of the rhombus are 16 and 12, we can substitute these values in the above equations to find the length of the sides of the rhombus.

Using the above equations, we can say that:

AC² = AB² + BC² = 16²
BD² = AB² + AD² = 12²

Now, we can solve the above equations to find the length of the sides of the rhombus. Let us solve the first equation:

AC² = AB² + BC² = 16²
AB = BC (as all sides of the rhombus are equal)

Substituting the value of BC as AB, we get:

AC² = AB² + AB² = 2AB²
AB² = AC²/2
AB = √(AC²/2)
AB = √128
AB = 8√2

Similarly, using the second equation, we can find the length of the other diagonal:

BD² = AB² + AD² = 12²
AB = AD (as all sides of the rhombus are equal)

Substituting the value of AD as AB, we get:

BD² = AB² + AB² = 2AB²
AB² = BD²/2
AB = √(BD²/2)
AB = √72
AB = 6√2

The Properties of a Rhombus

A rhombus has the following properties:

All sides of the rhombus are equal in length
The opposite sides of the rhombus are parallel to each other
The opposite angles of the rhombus are equal in measure
The diagonals of the rhombus bisect each other at right angles
The area of the rhombus can be calculated using the formula A = (d1 x d2)/2, where d1 and d2 are the lengths of the diagonals

Conclusion

In conclusion, the length of diagonals of a rhombus that are 16 and 12 can be calculated using the Pythagorean theorem. We can find the length of the sides of the rhombus using the length of the diagonals. A rhombus has several properties, including equal sides, parallel sides, equal angles, and diagonals that bisect each other at right angles. Understanding these properties can help us solve problems related to rhombuses.

So if you encounter any problem related to the length of diagonals of a rhombus, you can use the above method to find the length of the sides of the rhombus.