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The length of the diagonals of a rhombus are 16 cm and 12 cm respectively. find the length of each of its sides?
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The length of the diagonals of a rhombus are 16 cm and 12 cm respectiv...
Understanding the Rhombus
A rhombus is a special type of quadrilateral where all four sides are of equal length. The diagonals of a rhombus bisect each other at right angles. This property helps in calculating the length of each side when the lengths of the diagonals are known.
Given Diagonal Lengths
- Length of diagonal 1 (d1) = 16 cm
- Length of diagonal 2 (d2) = 12 cm
Finding the Half-Lengths of the Diagonals
Since the diagonals bisect each other:
- Half of diagonal 1 (d1/2) = 16 cm / 2 = 8 cm
- Half of diagonal 2 (d2/2) = 12 cm / 2 = 6 cm
Using the Pythagorean Theorem
To find the length of each side (s) of the rhombus, we can apply the Pythagorean theorem. Each side forms a right triangle with the halves of the diagonals:
- s² = (d1/2)² + (d2/2)²
- s² = 8² + 6²
- s² = 64 + 36
- s² = 100
Calculating the Length of the Side
Now, taking the square root of both sides:
- s = √100
- s = 10 cm
Conclusion
The length of each side of the rhombus is **10 cm**. This calculation demonstrates how the properties of the rhombus and the Pythagorean theorem can be utilized to find unknown lengths effectively.
A rhombus is a special type of quadrilateral where all four sides are of equal length. The diagonals of a rhombus bisect each other at right angles. This property helps in calculating the length of each side when the lengths of the diagonals are known.
Given Diagonal Lengths
- Length of diagonal 1 (d1) = 16 cm
- Length of diagonal 2 (d2) = 12 cm
Finding the Half-Lengths of the Diagonals
Since the diagonals bisect each other:
- Half of diagonal 1 (d1/2) = 16 cm / 2 = 8 cm
- Half of diagonal 2 (d2/2) = 12 cm / 2 = 6 cm
Using the Pythagorean Theorem
To find the length of each side (s) of the rhombus, we can apply the Pythagorean theorem. Each side forms a right triangle with the halves of the diagonals:
- s² = (d1/2)² + (d2/2)²
- s² = 8² + 6²
- s² = 64 + 36
- s² = 100
Calculating the Length of the Side
Now, taking the square root of both sides:
- s = √100
- s = 10 cm
Conclusion
The length of each side of the rhombus is **10 cm**. This calculation demonstrates how the properties of the rhombus and the Pythagorean theorem can be utilized to find unknown lengths effectively.
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The length of the diagonals of a rhombus are 16 cm and 12 cm respectively. find the length of each of its sides?
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The length of the diagonals of a rhombus are 16 cm and 12 cm respectively. find the length of each of its sides? for Class 8 2024 is part of Class 8 preparation. The Question and answers have been prepared according to the Class 8 exam syllabus. Information about The length of the diagonals of a rhombus are 16 cm and 12 cm respectively. find the length of each of its sides? covers all topics & solutions for Class 8 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The length of the diagonals of a rhombus are 16 cm and 12 cm respectively. find the length of each of its sides?.
The length of the diagonals of a rhombus are 16 cm and 12 cm respectively. find the length of each of its sides? for Class 8 2024 is part of Class 8 preparation. The Question and answers have been prepared according to the Class 8 exam syllabus. Information about The length of the diagonals of a rhombus are 16 cm and 12 cm respectively. find the length of each of its sides? covers all topics & solutions for Class 8 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The length of the diagonals of a rhombus are 16 cm and 12 cm respectively. find the length of each of its sides?.
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