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If area and perimeter of a rectangle is 6000 cm2 and 340 cm respectively, then the length of rectangle is:
- a)140
- b)120
- c)170
- d)200
Correct answer is option 'B'. Can you explain this answer?
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If area and perimeter of a rectangle is 6000 cm2and 340 cm respectivel...
Given:
Area of rectangle = 6000 cm²
Perimeter of rectangle = 340 cm
To find: Length of the rectangle
Solution:
Let the length of the rectangle be ‘l’ and its breadth be ‘b’.
Area of rectangle = l × b = 6000 cm²
Perimeter of rectangle = 2(l + b) = 340 cm
Solving the above two equations simultaneously, we get:
l + b = 170 (dividing both sides by 2)
l × b = 6000
We need to find the value of ‘l’. For that, we can use the fact that (l + b)² = l² + b² + 2lb
Expanding the above equation, we get:
l² + 2lb + b² = (l + b)²
l² + 2lb + b² = 170²
(l + b)² – 2lb = 170² – 2 × 6000
170² – 2lb = 100
lb = 170² – 10000
lb = 2890
We know that l × b = 6000
So, l = 6000/b
Substituting the value of ‘b’ from the above equation, we get:
l = 6000/2890 ≈ 2.0761 × 2890
l ≈ 6000/2890 ≈ 2.0761 × 2890
l ≈ 120 cm
Therefore, the length of the rectangle is 120 cm.
Hence, option (B) is the correct answer.
Area of rectangle = 6000 cm²
Perimeter of rectangle = 340 cm
To find: Length of the rectangle
Solution:
Let the length of the rectangle be ‘l’ and its breadth be ‘b’.
Area of rectangle = l × b = 6000 cm²
Perimeter of rectangle = 2(l + b) = 340 cm
Solving the above two equations simultaneously, we get:
l + b = 170 (dividing both sides by 2)
l × b = 6000
We need to find the value of ‘l’. For that, we can use the fact that (l + b)² = l² + b² + 2lb
Expanding the above equation, we get:
l² + 2lb + b² = (l + b)²
l² + 2lb + b² = 170²
(l + b)² – 2lb = 170² – 2 × 6000
170² – 2lb = 100
lb = 170² – 10000
lb = 2890
We know that l × b = 6000
So, l = 6000/b
Substituting the value of ‘b’ from the above equation, we get:
l = 6000/2890 ≈ 2.0761 × 2890
l ≈ 6000/2890 ≈ 2.0761 × 2890
l ≈ 120 cm
Therefore, the length of the rectangle is 120 cm.
Hence, option (B) is the correct answer.
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If area and perimeter of a rectangle is 6000 cm2and 340 cm respectively, then the length of rectangle is:a)140b)120c)170d)200Correct answer is option 'B'. Can you explain this answer?
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