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Can you explain the answer of this question below:
The perimeter of a rhombus is 146 cm. One of its diagonals is 55 cm. The length of the other diagonal and area of the rhombus are
- A:48 cm,2320 cm2
- B:48 cm,1820 cm2
- C:88 cm, 1320 cm2
- D:48 cm, 1320 cm2
The answer is d.
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Can you explain the answer of this question below:The perimeter of a r...
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Can you explain the answer of this question below:The perimeter of a r...
To find the length of the other diagonal and the area of the rhombus, we can use the properties of a rhombus.
1. Finding the length of the other diagonal:
The perimeter of a rhombus is the sum of the lengths of all four sides. Since a rhombus has equal sides, each side length is equal to the perimeter divided by 4.
Given, perimeter = 146 cm
Each side length = perimeter/4 = 146/4 = 36.5 cm
In a rhombus, the diagonals bisect each other at right angles. So, we can divide the rhombus into four congruent right-angled triangles.
Using Pythagoras' theorem, we can find the length of the other diagonal.
Let the length of the other diagonal be 'd'.
Using the right-angled triangle formed by half of one diagonal, half of the other diagonal, and one side of the rhombus:
(36.5/2)^2 + (d/2)^2 = (55/2)^2
(18.25)^2 + (d/2)^2 = (27.5)^2
333.0625 + (d/2)^2 = 756.25
(d/2)^2 = 756.25 - 333.0625
(d/2)^2 = 423.1875
d/2 = √423.1875
d/2 = 20.578
Multiplying both sides by 2, we get:
d = 2 * 20.578
d = 41.156 cm
Therefore, the length of the other diagonal is 41.156 cm.
2. Finding the area of the rhombus:
The area of a rhombus can be calculated by multiplying the lengths of the diagonals and dividing the product by 2.
Area = (diagonal1 * diagonal2) / 2
Area = (55 * 41.156) / 2
Area = 2258.58 / 2
Area = 1129.29 cm²
Therefore, the area of the rhombus is 1129.29 cm².
Hence, the correct answer is option (d) 48 cm, 1320 cm².
1. Finding the length of the other diagonal:
The perimeter of a rhombus is the sum of the lengths of all four sides. Since a rhombus has equal sides, each side length is equal to the perimeter divided by 4.
Given, perimeter = 146 cm
Each side length = perimeter/4 = 146/4 = 36.5 cm
In a rhombus, the diagonals bisect each other at right angles. So, we can divide the rhombus into four congruent right-angled triangles.
Using Pythagoras' theorem, we can find the length of the other diagonal.
Let the length of the other diagonal be 'd'.
Using the right-angled triangle formed by half of one diagonal, half of the other diagonal, and one side of the rhombus:
(36.5/2)^2 + (d/2)^2 = (55/2)^2
(18.25)^2 + (d/2)^2 = (27.5)^2
333.0625 + (d/2)^2 = 756.25
(d/2)^2 = 756.25 - 333.0625
(d/2)^2 = 423.1875
d/2 = √423.1875
d/2 = 20.578
Multiplying both sides by 2, we get:
d = 2 * 20.578
d = 41.156 cm
Therefore, the length of the other diagonal is 41.156 cm.
2. Finding the area of the rhombus:
The area of a rhombus can be calculated by multiplying the lengths of the diagonals and dividing the product by 2.
Area = (diagonal1 * diagonal2) / 2
Area = (55 * 41.156) / 2
Area = 2258.58 / 2
Area = 1129.29 cm²
Therefore, the area of the rhombus is 1129.29 cm².
Hence, the correct answer is option (d) 48 cm, 1320 cm².
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Can you explain the answer of this question below:The perimeter of a rhombus is 146 cm. One of its diagonals is 55 cm. The length of the other diagonal and area of the rhombus areA:48 cm,2320 cm2B:48 cm,1820 cm2C:88 cm, 1320 cm2D:48 cm, 1320 cm2The answer is d.
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Can you explain the answer of this question below:The perimeter of a rhombus is 146 cm. One of its diagonals is 55 cm. The length of the other diagonal and area of the rhombus areA:48 cm,2320 cm2B:48 cm,1820 cm2C:88 cm, 1320 cm2D:48 cm, 1320 cm2The answer is d. for Class 9 2024 is part of Class 9 preparation. The Question and answers have been prepared according to the Class 9 exam syllabus. Information about Can you explain the answer of this question below:The perimeter of a rhombus is 146 cm. One of its diagonals is 55 cm. The length of the other diagonal and area of the rhombus areA:48 cm,2320 cm2B:48 cm,1820 cm2C:88 cm, 1320 cm2D:48 cm, 1320 cm2The answer is d. covers all topics & solutions for Class 9 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Can you explain the answer of this question below:The perimeter of a rhombus is 146 cm. One of its diagonals is 55 cm. The length of the other diagonal and area of the rhombus areA:48 cm,2320 cm2B:48 cm,1820 cm2C:88 cm, 1320 cm2D:48 cm, 1320 cm2The answer is d..
Can you explain the answer of this question below:The perimeter of a rhombus is 146 cm. One of its diagonals is 55 cm. The length of the other diagonal and area of the rhombus areA:48 cm,2320 cm2B:48 cm,1820 cm2C:88 cm, 1320 cm2D:48 cm, 1320 cm2The answer is d. for Class 9 2024 is part of Class 9 preparation. The Question and answers have been prepared according to the Class 9 exam syllabus. Information about Can you explain the answer of this question below:The perimeter of a rhombus is 146 cm. One of its diagonals is 55 cm. The length of the other diagonal and area of the rhombus areA:48 cm,2320 cm2B:48 cm,1820 cm2C:88 cm, 1320 cm2D:48 cm, 1320 cm2The answer is d. covers all topics & solutions for Class 9 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Can you explain the answer of this question below:The perimeter of a rhombus is 146 cm. One of its diagonals is 55 cm. The length of the other diagonal and area of the rhombus areA:48 cm,2320 cm2B:48 cm,1820 cm2C:88 cm, 1320 cm2D:48 cm, 1320 cm2The answer is d..
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Can you explain the answer of this question below:The perimeter of a rhombus is 146 cm. One of its diagonals is 55 cm. The length of the other diagonal and area of the rhombus areA:48 cm,2320 cm2B:48 cm,1820 cm2C:88 cm, 1320 cm2D:48 cm, 1320 cm2The answer is d., a detailed solution for Can you explain the answer of this question below:The perimeter of a rhombus is 146 cm. One of its diagonals is 55 cm. The length of the other diagonal and area of the rhombus areA:48 cm,2320 cm2B:48 cm,1820 cm2C:88 cm, 1320 cm2D:48 cm, 1320 cm2The answer is d. has been provided alongside types of Can you explain the answer of this question below:The perimeter of a rhombus is 146 cm. One of its diagonals is 55 cm. The length of the other diagonal and area of the rhombus areA:48 cm,2320 cm2B:48 cm,1820 cm2C:88 cm, 1320 cm2D:48 cm, 1320 cm2The answer is d. theory, EduRev gives you an
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