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The area of a rectangular field whose length is three times its breadth is 348 m2. What is the perimeter of the field?
- a)82.16 m
- b)84.16 m
- c)86.16 m
- d)None of these
Correct answer is option 'C'. Can you explain this answer?
Most Upvoted Answer
The area of a rectangular field whose length is three times its breadt...
Let breadth be x m
∴ Length = 3x m
Now
∴
Perimeter = 2 (10.77 + 32.31) = 86.16 m
∴ Length = 3x m
Now
∴
Perimeter = 2 (10.77 + 32.31) = 86.16 m
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The area of a rectangular field whose length is three times its breadt...
Given:
Length of the field = 3 times its breadth
Area of the field = 348 m2
Let's assume the breadth of the field as 'x' meters.
So, the length of the field will be 3x meters.
To find the area of the field, we use the formula:
Area = Length × Breadth
348 = 3x × x
348 = 3x^2
Now, let's solve this quadratic equation to find the value of 'x'.
1. Dividing both sides of the equation by 3:
x^2 = 348/3
x^2 = 116
2. Taking the square root of both sides:
x = √116
x = 10.77 (approx.)
Therefore, the breadth of the field is approximately 10.77 meters.
Now, let's find the length of the field:
Length = 3x
Length = 3 × 10.77
Length = 32.31 (approx.)
Therefore, the length of the field is approximately 32.31 meters.
To find the perimeter of the field, we use the formula:
Perimeter = 2 × (Length + Breadth)
Calculating the perimeter:
Perimeter = 2 × (32.31 + 10.77)
Perimeter = 2 × 43.08
Perimeter = 86.16 meters
Therefore, the perimeter of the field is 86.16 meters.
Hence, the correct answer is option 'C'.
Length of the field = 3 times its breadth
Area of the field = 348 m2
Let's assume the breadth of the field as 'x' meters.
So, the length of the field will be 3x meters.
To find the area of the field, we use the formula:
Area = Length × Breadth
348 = 3x × x
348 = 3x^2
Now, let's solve this quadratic equation to find the value of 'x'.
1. Dividing both sides of the equation by 3:
x^2 = 348/3
x^2 = 116
2. Taking the square root of both sides:
x = √116
x = 10.77 (approx.)
Therefore, the breadth of the field is approximately 10.77 meters.
Now, let's find the length of the field:
Length = 3x
Length = 3 × 10.77
Length = 32.31 (approx.)
Therefore, the length of the field is approximately 32.31 meters.
To find the perimeter of the field, we use the formula:
Perimeter = 2 × (Length + Breadth)
Calculating the perimeter:
Perimeter = 2 × (32.31 + 10.77)
Perimeter = 2 × 43.08
Perimeter = 86.16 meters
Therefore, the perimeter of the field is 86.16 meters.
Hence, the correct answer is option 'C'.
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