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The ratio of the length and perimeter of a rectangle is 2:7. what is the ratio of the length and breadth of a rectangle?
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Understanding the Ratio of Length to Perimeter
The problem states that the ratio of the length (L) to the perimeter (P) of a rectangle is 2:7. To explore the implications of this ratio, we start by defining the perimeter of a rectangle.
- The formula for the perimeter of a rectangle is given by:
P = 2(L + B)
where B is the breadth of the rectangle.
Given the ratio of length to perimeter:
- L/P = 2/7
- This can be rearranged to express P in terms of L:
P = (7/2)L
Substituting for Perimeter
Substituting the expression for perimeter into the perimeter formula:
- (7/2)L = 2(L + B)
- Simplifying this gives:
7L = 4(L + B)
- Distributing the 4:
7L = 4L + 4B
- Rearranging leads to:
3L = 4B
Finding the Ratio of Length to Breadth
Now, we can express the ratio of length to breadth (L:B):
- Dividing both sides of the equation 3L = 4B by L and B respectively, we get:
L/B = 4/3
Thus, the ratio of the length to the breadth of the rectangle is:
Final Ratio
- L : B = 4 : 3
This indicates that for every 4 units of length, there are 3 units of breadth in the rectangle. This relationship holds true based on the initial ratio given for length and perimeter.
The problem states that the ratio of the length (L) to the perimeter (P) of a rectangle is 2:7. To explore the implications of this ratio, we start by defining the perimeter of a rectangle.
- The formula for the perimeter of a rectangle is given by:
P = 2(L + B)
where B is the breadth of the rectangle.
Given the ratio of length to perimeter:
- L/P = 2/7
- This can be rearranged to express P in terms of L:
P = (7/2)L
Substituting for Perimeter
Substituting the expression for perimeter into the perimeter formula:
- (7/2)L = 2(L + B)
- Simplifying this gives:
7L = 4(L + B)
- Distributing the 4:
7L = 4L + 4B
- Rearranging leads to:
3L = 4B
Finding the Ratio of Length to Breadth
Now, we can express the ratio of length to breadth (L:B):
- Dividing both sides of the equation 3L = 4B by L and B respectively, we get:
L/B = 4/3
Thus, the ratio of the length to the breadth of the rectangle is:
Final Ratio
- L : B = 4 : 3
This indicates that for every 4 units of length, there are 3 units of breadth in the rectangle. This relationship holds true based on the initial ratio given for length and perimeter.
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The ratio of the length and perimeter of a rectangle is 2:7. what is the ratio of the length and breadth of a rectangle?
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The ratio of the length and perimeter of a rectangle is 2:7. what is the ratio of the length and breadth of a rectangle? for SSC CGL 2024 is part of SSC CGL preparation. The Question and answers have been prepared according to the SSC CGL exam syllabus. Information about The ratio of the length and perimeter of a rectangle is 2:7. what is the ratio of the length and breadth of a rectangle? covers all topics & solutions for SSC CGL 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The ratio of the length and perimeter of a rectangle is 2:7. what is the ratio of the length and breadth of a rectangle?.
The ratio of the length and perimeter of a rectangle is 2:7. what is the ratio of the length and breadth of a rectangle? for SSC CGL 2024 is part of SSC CGL preparation. The Question and answers have been prepared according to the SSC CGL exam syllabus. Information about The ratio of the length and perimeter of a rectangle is 2:7. what is the ratio of the length and breadth of a rectangle? covers all topics & solutions for SSC CGL 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The ratio of the length and perimeter of a rectangle is 2:7. what is the ratio of the length and breadth of a rectangle?.
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