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The length of the rectangle is greater than breadth by 3 cm .if the length is increased by 9cm and the breadth is reduced by 5cm ,the area remains the same.find the dimensions of the rectangle?
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The length of the rectangle is greater than breadth by 3 cm .if the le...
Problem Statement
We have a rectangle where the length exceeds the breadth by 3 cm. If the length is increased by 9 cm and the breadth is decreased by 5 cm, the area remains unchanged. We need to find the dimensions of the rectangle.
Let’s Define Variables
- Let the breadth of the rectangle be represented as "b" cm.
- Therefore, the length can be expressed as "l = b + 3" cm.
Original Area
- The original area of the rectangle can be calculated as:
- Area = Length × Breadth
- Area = (b + 3) × b
New Dimensions
- After the changes:
- New Length = (b + 3) + 9 = b + 12 cm
- New Breadth = b - 5 cm
Area After Changes
- The area with new dimensions is:
- New Area = New Length × New Breadth
- New Area = (b + 12) × (b - 5)
Setting Up the Equation
- Since the area remains the same:
- (b + 3) × b = (b + 12) × (b - 5)
Expanding the Equation
- Expanding both sides:
- b^2 + 3b = b^2 + 12b - 5b - 60
Simplifying the Equation
- This reduces to:
- 3b = 7b - 60
- 60 = 4b
- b = 15 cm
Calculating Length
- Now, substituting back to find the length:
- l = b + 3 = 15 + 3 = 18 cm
Final Dimensions
- Therefore, the dimensions of the rectangle are:
- Breadth = 15 cm
- Length = 18 cm
We have a rectangle where the length exceeds the breadth by 3 cm. If the length is increased by 9 cm and the breadth is decreased by 5 cm, the area remains unchanged. We need to find the dimensions of the rectangle.
Let’s Define Variables
- Let the breadth of the rectangle be represented as "b" cm.
- Therefore, the length can be expressed as "l = b + 3" cm.
Original Area
- The original area of the rectangle can be calculated as:
- Area = Length × Breadth
- Area = (b + 3) × b
New Dimensions
- After the changes:
- New Length = (b + 3) + 9 = b + 12 cm
- New Breadth = b - 5 cm
Area After Changes
- The area with new dimensions is:
- New Area = New Length × New Breadth
- New Area = (b + 12) × (b - 5)
Setting Up the Equation
- Since the area remains the same:
- (b + 3) × b = (b + 12) × (b - 5)
Expanding the Equation
- Expanding both sides:
- b^2 + 3b = b^2 + 12b - 5b - 60
Simplifying the Equation
- This reduces to:
- 3b = 7b - 60
- 60 = 4b
- b = 15 cm
Calculating Length
- Now, substituting back to find the length:
- l = b + 3 = 15 + 3 = 18 cm
Final Dimensions
- Therefore, the dimensions of the rectangle are:
- Breadth = 15 cm
- Length = 18 cm
Community Answer
The length of the rectangle is greater than breadth by 3 cm .if the le...
18cm,15cm
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The length of the rectangle is greater than breadth by 3 cm .if the length is increased by 9cm and the breadth is reduced by 5cm ,the area remains the same.find the dimensions of the rectangle?
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The length of the rectangle is greater than breadth by 3 cm .if the length is increased by 9cm and the breadth is reduced by 5cm ,the area remains the same.find the dimensions of the rectangle? for Class 8 2024 is part of Class 8 preparation. The Question and answers have been prepared according to the Class 8 exam syllabus. Information about The length of the rectangle is greater than breadth by 3 cm .if the length is increased by 9cm and the breadth is reduced by 5cm ,the area remains the same.find the dimensions of the rectangle? covers all topics & solutions for Class 8 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The length of the rectangle is greater than breadth by 3 cm .if the length is increased by 9cm and the breadth is reduced by 5cm ,the area remains the same.find the dimensions of the rectangle?.
The length of the rectangle is greater than breadth by 3 cm .if the length is increased by 9cm and the breadth is reduced by 5cm ,the area remains the same.find the dimensions of the rectangle? for Class 8 2024 is part of Class 8 preparation. The Question and answers have been prepared according to the Class 8 exam syllabus. Information about The length of the rectangle is greater than breadth by 3 cm .if the length is increased by 9cm and the breadth is reduced by 5cm ,the area remains the same.find the dimensions of the rectangle? covers all topics & solutions for Class 8 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The length of the rectangle is greater than breadth by 3 cm .if the length is increased by 9cm and the breadth is reduced by 5cm ,the area remains the same.find the dimensions of the rectangle?.
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