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Difference between the length and breadth of a field is 48 metres and its perimeter is of 160 metres. What would be the length of a side of a square whose area is equal to this field ?
- a)32 metre
- b)16 metre
- c)64 metre
- d)48 metre
Correct answer is option 'A'. Can you explain this answer?
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Verified Answer
Difference between the length and breadth of a field is 48 metres and ...
l - b = 48
(l+b)*2 = 160
So, l = 64
b = 16
Area of the rectangle = area of the square = 64 x 16
Side of the square = sq root (64 x 16) = 8 x 4 = 32
Most Upvoted Answer
Difference between the length and breadth of a field is 48 metres and ...
Given:
- The difference between the length and breadth of the field is 48 meters.
- The perimeter of the field is 160 meters.
To find:
The length of a side of a square whose area is equal to the field.
Let's assume:
- Length of the field = L meters
- Breadth of the field = B meters
From the given information, we can form the following equations:
1. L - B = 48 --- (Equation 1)
2. 2(L + B) = 160 --- (Equation 2)
Simplifying Equation 2, we get:
L + B = 80 --- (Equation 3)
Adding Equation 1 and Equation 3, we get:
2L = 128
Dividing by 2 on both sides, we get:
L = 64
Substituting the value of L in Equation 3, we get:
64 + B = 80
Simplifying, we get:
B = 16
Therefore, the length of the field is 64 meters and the breadth of the field is 16 meters.
To find the length of a side of a square with the same area as the field, we need to find the area of the field first.
Area of the field = Length × Breadth
= 64 × 16
= 1024 square meters
The area of the square is also equal to 1024 square meters.
Let's assume:
- Side length of the square = S meters
To find the side length of the square, we can use the formula for the area of a square:
Area of the square = Side length × Side length
1024 = S × S
Taking the square root of both sides, we get:
√1024 = S
Simplifying, we get:
32 = S
Therefore, the length of a side of the square with the same area as the field is 32 meters.
Hence, the correct answer is option A) 32 meters.
- The difference between the length and breadth of the field is 48 meters.
- The perimeter of the field is 160 meters.
To find:
The length of a side of a square whose area is equal to the field.
Let's assume:
- Length of the field = L meters
- Breadth of the field = B meters
From the given information, we can form the following equations:
1. L - B = 48 --- (Equation 1)
2. 2(L + B) = 160 --- (Equation 2)
Simplifying Equation 2, we get:
L + B = 80 --- (Equation 3)
Adding Equation 1 and Equation 3, we get:
2L = 128
Dividing by 2 on both sides, we get:
L = 64
Substituting the value of L in Equation 3, we get:
64 + B = 80
Simplifying, we get:
B = 16
Therefore, the length of the field is 64 meters and the breadth of the field is 16 meters.
To find the length of a side of a square with the same area as the field, we need to find the area of the field first.
Area of the field = Length × Breadth
= 64 × 16
= 1024 square meters
The area of the square is also equal to 1024 square meters.
Let's assume:
- Side length of the square = S meters
To find the side length of the square, we can use the formula for the area of a square:
Area of the square = Side length × Side length
1024 = S × S
Taking the square root of both sides, we get:
√1024 = S
Simplifying, we get:
32 = S
Therefore, the length of a side of the square with the same area as the field is 32 meters.
Hence, the correct answer is option A) 32 meters.
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Difference between the length and breadth of a field is 48 metres and its perimeter is of 160 metres. What would be the length of a side of a square whose area is equal to this field ?a)32 metreb)16 metrec)64 metred)48 metreCorrect answer is option 'A'. Can you explain this answer?
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