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Find the perimeter of a rhombus which diagonal measures 16 cm and 30 cm?
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Find the perimeter of a rhombus which diagonal measures 16 cm and 30 c...
To find the perimeter of a rhombus given its diagonals, follow the detailed steps below.
Understanding the Rhombus
- A rhombus is a quadrilateral with all sides of equal length.
- The diagonals of a rhombus bisect each other at right angles.
Given Dimensions
- Diagonal 1 (d1) = 16 cm
- Diagonal 2 (d2) = 30 cm
Finding the Length of the Sides
1. Calculate Half of Each Diagonal:
- Half of Diagonal 1 (d1/2) = 16 cm / 2 = 8 cm
- Half of Diagonal 2 (d2/2) = 30 cm / 2 = 15 cm
2. Using the Pythagorean Theorem:
- Each side of the rhombus can be found using the formula:
\[
\text{Side} = \sqrt{(d1/2)^2 + (d2/2)^2}
\]
- Plugging in the values:
\[
\text{Side} = \sqrt{(8)^2 + (15)^2} = \sqrt{64 + 225} = \sqrt{289} = 17 \text{ cm}
\]
Calculating the Perimeter
- The perimeter (P) of a rhombus is given by:
\[
P = 4 \times \text{Side}
\]
- Therefore:
\[
P = 4 \times 17 \text{ cm} = 68 \text{ cm}
\]
Final Result
- The perimeter of the rhombus with diagonals measuring 16 cm and 30 cm is 68 cm.
Understanding the Rhombus
- A rhombus is a quadrilateral with all sides of equal length.
- The diagonals of a rhombus bisect each other at right angles.
Given Dimensions
- Diagonal 1 (d1) = 16 cm
- Diagonal 2 (d2) = 30 cm
Finding the Length of the Sides
1. Calculate Half of Each Diagonal:
- Half of Diagonal 1 (d1/2) = 16 cm / 2 = 8 cm
- Half of Diagonal 2 (d2/2) = 30 cm / 2 = 15 cm
2. Using the Pythagorean Theorem:
- Each side of the rhombus can be found using the formula:
\[
\text{Side} = \sqrt{(d1/2)^2 + (d2/2)^2}
\]
- Plugging in the values:
\[
\text{Side} = \sqrt{(8)^2 + (15)^2} = \sqrt{64 + 225} = \sqrt{289} = 17 \text{ cm}
\]
Calculating the Perimeter
- The perimeter (P) of a rhombus is given by:
\[
P = 4 \times \text{Side}
\]
- Therefore:
\[
P = 4 \times 17 \text{ cm} = 68 \text{ cm}
\]
Final Result
- The perimeter of the rhombus with diagonals measuring 16 cm and 30 cm is 68 cm.
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Find the perimeter of a rhombus which diagonal measures 16 cm and 30 cm?
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Find the perimeter of a rhombus which diagonal measures 16 cm and 30 cm? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about Find the perimeter of a rhombus which diagonal measures 16 cm and 30 cm? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Find the perimeter of a rhombus which diagonal measures 16 cm and 30 cm?.
Find the perimeter of a rhombus which diagonal measures 16 cm and 30 cm? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about Find the perimeter of a rhombus which diagonal measures 16 cm and 30 cm? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Find the perimeter of a rhombus which diagonal measures 16 cm and 30 cm?.
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