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The perimeter of a rhombus is 20 cm. One of its diagonals is 8 cm. Then area of the rhombus is
- a)24 cm2
- b)42 cm2
- c)18 cm2
- d)36 cm2
Correct answer is option 'A'. Can you explain this answer?
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Verified Answer
The perimeter of a rhombus is 20 cm. One of its diagonals is 8 cm. The...
Given, Perimeter of a rhombus = 20 cm
Perimeter of a rhombus = 4*side
Hence, side = 20/4 = 5 cm.
Now, we know that the diagonals of a rhombus bisect each other at right angles (90 degree).
Hence 'a right angled triangle can be visualised with 'side' as the hypotenuse'.
diagonal length = 8 cm
Half the length (since diagonal bisects each other) = 8/2 = 4 cm
(d/2)^2 + (d1/2)^2 = 5^2
4^2 + (d1/2)^2 = 5^2
(d1/2)^2 = 9
d1/2 = 3
d1 = 3*2 = 6 cm
Hence other diagonal = 6 cm.
Area = 1/2 * d1*d = 1/2 * 8 * 6 = 24 cm^2
Hope it helps.
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The perimeter of a rhombus is 20 cm. One of its diagonals is 8 cm. The...
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The perimeter of a rhombus is 20 cm. One of its diagonals is 8 cm. The...
Given:
Perimeter of the rhombus = 20 cm
Length of one diagonal of the rhombus = 8 cm
To Find:
Area of the rhombus
Solution:
To find the area of the rhombus, we need to know the length of both diagonals. However, we are only given the length of one diagonal. Therefore, we need to find the length of the other diagonal.
Finding the Length of the Other Diagonal:
In a rhombus, the diagonals bisect each other at right angles and divide the rhombus into four congruent right-angled triangles.
Using the Pythagorean theorem, we can find the length of the other diagonal.
Let the other diagonal be 'd'.
Using the given diagonal (8 cm) and the side length (perimeter/4 = 20/4 = 5 cm) of the rhombus, we can find the length of the other diagonal using the formula:
d^2 = (8/2)^2 + 5^2
d^2 = 4^2 + 5^2
d^2 = 16 + 25
d^2 = 41
Taking the square root of both sides:
d = √41
Calculating the Area:
The area of a rhombus can be calculated using the formula:
Area = (diagonal1 * diagonal2) / 2
Substituting the values:
Area = (8 * √41) / 2
Area = 4 * √41
Approximating the value of √41:
√41 ≈ 6.4
Area ≈ 4 * 6.4
Area ≈ 25.6
Therefore, the approximate area of the rhombus is 25.6 cm².
Conclusion:
The correct answer is not among the given options. It seems there may be an error in the provided options.
Perimeter of the rhombus = 20 cm
Length of one diagonal of the rhombus = 8 cm
To Find:
Area of the rhombus
Solution:
To find the area of the rhombus, we need to know the length of both diagonals. However, we are only given the length of one diagonal. Therefore, we need to find the length of the other diagonal.
Finding the Length of the Other Diagonal:
In a rhombus, the diagonals bisect each other at right angles and divide the rhombus into four congruent right-angled triangles.
Using the Pythagorean theorem, we can find the length of the other diagonal.
Let the other diagonal be 'd'.
Using the given diagonal (8 cm) and the side length (perimeter/4 = 20/4 = 5 cm) of the rhombus, we can find the length of the other diagonal using the formula:
d^2 = (8/2)^2 + 5^2
d^2 = 4^2 + 5^2
d^2 = 16 + 25
d^2 = 41
Taking the square root of both sides:
d = √41
Calculating the Area:
The area of a rhombus can be calculated using the formula:
Area = (diagonal1 * diagonal2) / 2
Substituting the values:
Area = (8 * √41) / 2
Area = 4 * √41
Approximating the value of √41:
√41 ≈ 6.4
Area ≈ 4 * 6.4
Area ≈ 25.6
Therefore, the approximate area of the rhombus is 25.6 cm².
Conclusion:
The correct answer is not among the given options. It seems there may be an error in the provided options.
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The perimeter of a rhombus is 20 cm. One of its diagonals is 8 cm. Then area of the rhombus isa)24cm2b)42 cm2c)18cm2d)36cm2Correct answer is option 'A'. Can you explain this answer?
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