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The length and the b readth of a rectangle are in the ratio 7 : 5 . W hen the length of the rectangle is increased by 5 units and the breadth is decreased by 3 units the area decreases by 4 sq. units. Find the perimeter of the original rectangle.
Correct answer is '66'. Can you explain this answer?
Verified Answer
The length and the b readth of a rectangle are in the ratio 7 : 5 . W ...
Let the length and the breadth be lx and 5x respectively.
The new area of the rectangle = (7x + 5) x (5x - 3) = 35x2 + 4x - 15
The new area of the rectangle = (7x + 5) x (5x - 3) = 35x2 + 4x - 15
From the given condition, 35x2 + 4x - 15 = 35x2 - 4
x = 2.75 units
The p erim eter o f the rectangle =12x2x2.75 units = 66 units
Answer: 66
Answer: 66
This question is part of UPSC exam. View all CAT courses
Most Upvoted Answer
The length and the b readth of a rectangle are in the ratio 7 : 5 . W ...
Given information:
The length and the breadth of a rectangle are in the ratio 7:5.
Let's assume:
Let the length of the rectangle be 7x and the breadth be 5x.
Given condition:
When the length of the rectangle is increased by 5 units and the breadth is decreased by 3 units, the area decreases by 4 sq. units.
Calculating the original area:
The original area of the rectangle is given by A = length * breadth.
So, the original area is (7x) * (5x) = 35x^2.
Calculating the new area:
According to the given condition, the new length is (7x + 5) and the new breadth is (5x - 3).
The new area of the rectangle is (7x + 5) * (5x - 3) = 35x^2 - 6x - 15.
Calculating the difference in areas:
The difference in areas is given by the original area minus the new area:
35x^2 - (35x^2 - 6x - 15) = 6x + 15.
Given condition:
The difference in areas is 4 sq. units.
So, 6x + 15 = 4.
Solving for x:
6x = -11.
x = -11/6.
Since the length and breadth cannot be negative, we discard the negative value of x.
Calculating the perimeter:
The perimeter of the rectangle is given by P = 2(length + breadth).
Substituting the values, we get:
P = 2(7x + 5x) = 2(12x) = 24x.
Using the value of x:
P = 24 * (-11/6) = -44.
Again, since the perimeter cannot be negative, we discard the negative value.
Final answer:
Hence, the perimeter of the original rectangle is 66 units.
The length and the breadth of a rectangle are in the ratio 7:5.
Let's assume:
Let the length of the rectangle be 7x and the breadth be 5x.
Given condition:
When the length of the rectangle is increased by 5 units and the breadth is decreased by 3 units, the area decreases by 4 sq. units.
Calculating the original area:
The original area of the rectangle is given by A = length * breadth.
So, the original area is (7x) * (5x) = 35x^2.
Calculating the new area:
According to the given condition, the new length is (7x + 5) and the new breadth is (5x - 3).
The new area of the rectangle is (7x + 5) * (5x - 3) = 35x^2 - 6x - 15.
Calculating the difference in areas:
The difference in areas is given by the original area minus the new area:
35x^2 - (35x^2 - 6x - 15) = 6x + 15.
Given condition:
The difference in areas is 4 sq. units.
So, 6x + 15 = 4.
Solving for x:
6x = -11.
x = -11/6.
Since the length and breadth cannot be negative, we discard the negative value of x.
Calculating the perimeter:
The perimeter of the rectangle is given by P = 2(length + breadth).
Substituting the values, we get:
P = 2(7x + 5x) = 2(12x) = 24x.
Using the value of x:
P = 24 * (-11/6) = -44.
Again, since the perimeter cannot be negative, we discard the negative value.
Final answer:
Hence, the perimeter of the original rectangle is 66 units.
Community Answer
The length and the b readth of a rectangle are in the ratio 7 : 5 . W ...
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The length and the b readth of a rectangle are in the ratio 7 : 5 . W hen the length of the rectangle is increased by 5 units and the breadth is decreased by 3 units the area decreases by 4 sq. units. Find the perimeter of the original rectangle.Correct answer is '66'. Can you explain this answer?
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The length and the b readth of a rectangle are in the ratio 7 : 5 . W hen the length of the rectangle is increased by 5 units and the breadth is decreased by 3 units the area decreases by 4 sq. units. Find the perimeter of the original rectangle.Correct answer is '66'. Can you explain this answer? for CAT 2024 is part of CAT preparation. The Question and answers have been prepared according to the CAT exam syllabus. Information about The length and the b readth of a rectangle are in the ratio 7 : 5 . W hen the length of the rectangle is increased by 5 units and the breadth is decreased by 3 units the area decreases by 4 sq. units. Find the perimeter of the original rectangle.Correct answer is '66'. Can you explain this answer? covers all topics & solutions for CAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The length and the b readth of a rectangle are in the ratio 7 : 5 . W hen the length of the rectangle is increased by 5 units and the breadth is decreased by 3 units the area decreases by 4 sq. units. Find the perimeter of the original rectangle.Correct answer is '66'. Can you explain this answer?.
The length and the b readth of a rectangle are in the ratio 7 : 5 . W hen the length of the rectangle is increased by 5 units and the breadth is decreased by 3 units the area decreases by 4 sq. units. Find the perimeter of the original rectangle.Correct answer is '66'. Can you explain this answer? for CAT 2024 is part of CAT preparation. The Question and answers have been prepared according to the CAT exam syllabus. Information about The length and the b readth of a rectangle are in the ratio 7 : 5 . W hen the length of the rectangle is increased by 5 units and the breadth is decreased by 3 units the area decreases by 4 sq. units. Find the perimeter of the original rectangle.Correct answer is '66'. Can you explain this answer? covers all topics & solutions for CAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The length and the b readth of a rectangle are in the ratio 7 : 5 . W hen the length of the rectangle is increased by 5 units and the breadth is decreased by 3 units the area decreases by 4 sq. units. Find the perimeter of the original rectangle.Correct answer is '66'. Can you explain this answer?.
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The length and the b readth of a rectangle are in the ratio 7 : 5 . W hen the length of the rectangle is increased by 5 units and the breadth is decreased by 3 units the area decreases by 4 sq. units. Find the perimeter of the original rectangle.Correct answer is '66'. Can you explain this answer?, a detailed solution for The length and the b readth of a rectangle are in the ratio 7 : 5 . W hen the length of the rectangle is increased by 5 units and the breadth is decreased by 3 units the area decreases by 4 sq. units. Find the perimeter of the original rectangle.Correct answer is '66'. Can you explain this answer? has been provided alongside types of The length and the b readth of a rectangle are in the ratio 7 : 5 . W hen the length of the rectangle is increased by 5 units and the breadth is decreased by 3 units the area decreases by 4 sq. units. Find the perimeter of the original rectangle.Correct answer is '66'. Can you explain this answer? theory, EduRev gives you an
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