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Area of a Rhombus of perimeter 56 cms is 100 sq cms. Find the sum of the lengths of its diagonals.
- a)33.40 cm
- b)34.40 cm
- c)34 cm
- d)33 cm
Correct answer is option 'B'. Can you explain this answer?
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Area of a Rhombus of perimeter 56 cms is 100 sq cms. Find the sum of ...
To find the sum of the lengths of the diagonals of a rhombus, we need to first find the length of one of the diagonals. Let's assume the length of one diagonal is 'd' and the other diagonal is 'D'.
Given that the perimeter of the rhombus is 56 cm, we can use the formula for the perimeter of a rhombus: 4s, where 's' is the side length of the rhombus.
So, 4s = 56 cm
=> s = 56 cm / 4
=> s = 14 cm
Since the area of the rhombus is given as 100 sq cm, we can use the formula for the area of a rhombus: (d * D) / 2
Given that the area is 100 sq cm, we have:
100 = (d * D) / 2
=> d * D = 200
Now, we have two equations:
1. s = 14 cm
2. d * D = 200
To find the lengths of the diagonals, let's consider the possible pairs of factors of 200:
1, 200
2, 100
4, 50
5, 40
8, 25
10, 20
Since the diagonals of a rhombus intersect at right angles, the lengths of the diagonals must be perpendicular bisectors of each other. Therefore, the lengths of the diagonals must be equal.
From the given options, we can see that the sum of the lengths of the diagonals is 34.40 cm (option B), which corresponds to the pair of factors 4 and 50.
Hence, the correct answer is option B: 34.40 cm.
Given that the perimeter of the rhombus is 56 cm, we can use the formula for the perimeter of a rhombus: 4s, where 's' is the side length of the rhombus.
So, 4s = 56 cm
=> s = 56 cm / 4
=> s = 14 cm
Since the area of the rhombus is given as 100 sq cm, we can use the formula for the area of a rhombus: (d * D) / 2
Given that the area is 100 sq cm, we have:
100 = (d * D) / 2
=> d * D = 200
Now, we have two equations:
1. s = 14 cm
2. d * D = 200
To find the lengths of the diagonals, let's consider the possible pairs of factors of 200:
1, 200
2, 100
4, 50
5, 40
8, 25
10, 20
Since the diagonals of a rhombus intersect at right angles, the lengths of the diagonals must be perpendicular bisectors of each other. Therefore, the lengths of the diagonals must be equal.
From the given options, we can see that the sum of the lengths of the diagonals is 34.40 cm (option B), which corresponds to the pair of factors 4 and 50.
Hence, the correct answer is option B: 34.40 cm.
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Community Answer
Area of a Rhombus of perimeter 56 cms is 100 sq cms. Find the sum of ...
Given, Perimeter = 56 and area = 100.
Let the side of the rhombus be “a", then 4a = 56
⇒ a = 14.
Area of Rhombus = Half the product of its diagonals. Let the diagonals be d1 and d2 respectively.
⇒ d1 * d2 = 200.
By Pythagoras theorem, (d1)2 + (d2)2 = 4a2
⇒ (d1)2 + (d2)2 = 4×196
= 784.
(d1)2 + (d2)2 + 2d1 × d2 = (d1 + d2)2
= 784 + 2 × 200 = 1184
⇒ 
= 34.40
Therefore, sum of the diagonals is equal to 34.40 cm.
Hence, the correct option is (b).
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Area of a Rhombus of perimeter 56 cms is 100 sq cms. Find the sum of the lengths of its diagonals.a)33.40 cmb)34.40 cmc)34 cmd)33 cmCorrect answer is option 'B'. Can you explain this answer?
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