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The perimeter of a rhombus with one diagonal 24 cm long is the same as the perimeter of an equilateral triangle with side 20 cm find the length of the other diagonal?
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The perimeter of a rhombus with one diagonal 24 cm long is the same as...
Understanding the Problem
To find the length of the other diagonal of the rhombus, we first need to establish the perimeter of the equilateral triangle and relate it to the rhombus.
Step 1: Perimeter of the Equilateral Triangle
- The side of the equilateral triangle = 20 cm
- Perimeter of the triangle = 3 × side = 3 × 20 = 60 cm
Step 2: Perimeter of the Rhombus
- Since the perimeter of the rhombus is equal to the perimeter of the triangle, the perimeter of the rhombus = 60 cm.
- Let the length of each side of the rhombus be ‘s’. Thus, 4s = 60.
- Solving for s gives us s = 15 cm.
Step 3: Relationship Between Diagonals
- In a rhombus, the diagonals bisect each other at right angles.
- Let the lengths of the diagonals be d1 and d2. Here, d1 = 24 cm and we need to find d2.
- Using the formula for the sides of the rhombus in terms of the diagonals:
s = √((d1/2)² + (d2/2)²).
Step 4: Calculation
- Substituting the known values:
15 = √((24/2)² + (d2/2)²)
15 = √(12² + (d2/2)²)
15 = √(144 + (d2/2)²).
- Squaring both sides:
225 = 144 + (d2/2)²
81 = (d2/2)².
- Taking the square root gives:
d2/2 = 9, thus d2 = 18 cm.
Conclusion
The length of the other diagonal of the rhombus is 18 cm.
To find the length of the other diagonal of the rhombus, we first need to establish the perimeter of the equilateral triangle and relate it to the rhombus.
Step 1: Perimeter of the Equilateral Triangle
- The side of the equilateral triangle = 20 cm
- Perimeter of the triangle = 3 × side = 3 × 20 = 60 cm
Step 2: Perimeter of the Rhombus
- Since the perimeter of the rhombus is equal to the perimeter of the triangle, the perimeter of the rhombus = 60 cm.
- Let the length of each side of the rhombus be ‘s’. Thus, 4s = 60.
- Solving for s gives us s = 15 cm.
Step 3: Relationship Between Diagonals
- In a rhombus, the diagonals bisect each other at right angles.
- Let the lengths of the diagonals be d1 and d2. Here, d1 = 24 cm and we need to find d2.
- Using the formula for the sides of the rhombus in terms of the diagonals:
s = √((d1/2)² + (d2/2)²).
Step 4: Calculation
- Substituting the known values:
15 = √((24/2)² + (d2/2)²)
15 = √(12² + (d2/2)²)
15 = √(144 + (d2/2)²).
- Squaring both sides:
225 = 144 + (d2/2)²
81 = (d2/2)².
- Taking the square root gives:
d2/2 = 9, thus d2 = 18 cm.
Conclusion
The length of the other diagonal of the rhombus is 18 cm.
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The perimeter of a rhombus with one diagonal 24 cm long is the same as the perimeter of an equilateral triangle with side 20 cm find the length of the other diagonal?
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The perimeter of a rhombus with one diagonal 24 cm long is the same as the perimeter of an equilateral triangle with side 20 cm find the length of the other diagonal? 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 perimeter of a rhombus with one diagonal 24 cm long is the same as the perimeter of an equilateral triangle with side 20 cm find the length of the other diagonal? covers all topics & solutions for Class 8 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The perimeter of a rhombus with one diagonal 24 cm long is the same as the perimeter of an equilateral triangle with side 20 cm find the length of the other diagonal?.
The perimeter of a rhombus with one diagonal 24 cm long is the same as the perimeter of an equilateral triangle with side 20 cm find the length of the other diagonal? 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 perimeter of a rhombus with one diagonal 24 cm long is the same as the perimeter of an equilateral triangle with side 20 cm find the length of the other diagonal? covers all topics & solutions for Class 8 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The perimeter of a rhombus with one diagonal 24 cm long is the same as the perimeter of an equilateral triangle with side 20 cm find the length of the other diagonal?.
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