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The diagonals of a rhombus are 18 cm and 24 cm find the perimeter of rhombus?
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The diagonals of a rhombus are 18 cm and 24 cm find the perimeter of r...
Understanding the Rhombus
A rhombus is a type of polygon that is a quadrilateral (four sides) with all sides equal in length. The diagonals of a rhombus intersect at right angles and bisect each other, creating four right-angled triangles.
Given Dimensions
- Length of diagonal 1 (d1) = 18 cm
- Length of diagonal 2 (d2) = 24 cm
Finding the Length of One Side
1. Calculate the Half-Lengths of Diagonals:
- Half of diagonal 1 (d1/2) = 18 cm / 2 = 9 cm
- Half of diagonal 2 (d2/2) = 24 cm / 2 = 12 cm
2. Use the Pythagorean Theorem:
Each half diagonal and a side of the rhombus form a right triangle.
- Let s be the length of one side of the rhombus.
- According to the Pythagorean theorem:
s = √((d1/2)² + (d2/2)²)
= √(9² + 12²)
= √(81 + 144)
= √225
= 15 cm
Calculating the Perimeter
- Formula for Perimeter (P) of a Rhombus:
P = 4 * s
- Substituting the Side Length:
P = 4 * 15 cm = 60 cm
Conclusion
The perimeter of the rhombus is 60 cm.
A rhombus is a type of polygon that is a quadrilateral (four sides) with all sides equal in length. The diagonals of a rhombus intersect at right angles and bisect each other, creating four right-angled triangles.
Given Dimensions
- Length of diagonal 1 (d1) = 18 cm
- Length of diagonal 2 (d2) = 24 cm
Finding the Length of One Side
1. Calculate the Half-Lengths of Diagonals:
- Half of diagonal 1 (d1/2) = 18 cm / 2 = 9 cm
- Half of diagonal 2 (d2/2) = 24 cm / 2 = 12 cm
2. Use the Pythagorean Theorem:
Each half diagonal and a side of the rhombus form a right triangle.
- Let s be the length of one side of the rhombus.
- According to the Pythagorean theorem:
s = √((d1/2)² + (d2/2)²)
= √(9² + 12²)
= √(81 + 144)
= √225
= 15 cm
Calculating the Perimeter
- Formula for Perimeter (P) of a Rhombus:
P = 4 * s
- Substituting the Side Length:
P = 4 * 15 cm = 60 cm
Conclusion
The perimeter of the rhombus is 60 cm.
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The diagonals of a rhombus are 18 cm and 24 cm find the perimeter of rhombus?
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The diagonals of a rhombus are 18 cm and 24 cm find the perimeter of rhombus? 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 diagonals of a rhombus are 18 cm and 24 cm find the perimeter of rhombus? covers all topics & solutions for Class 8 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The diagonals of a rhombus are 18 cm and 24 cm find the perimeter of rhombus?.
The diagonals of a rhombus are 18 cm and 24 cm find the perimeter of rhombus? 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 diagonals of a rhombus are 18 cm and 24 cm find the perimeter of rhombus? covers all topics & solutions for Class 8 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The diagonals of a rhombus are 18 cm and 24 cm find the perimeter of rhombus?.
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