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The perimeter of a rectangle is 240 CM if the length is decreased by 10% and the breadth is increased by 20% we get the same perimeter find the length and breadth of the rectangle?
Verified Answer
The perimeter of a rectangle is 240 CM if the length is decreased by 1...
Let the dimensions of the
rectangle are
i) length = x cm
breadth = y cm
Perimeter = 240 cm ( given )
2( x + y ) = 240
x + y = 120 ----( 1 )
If length is decreased by 10% and
breadth is increased by 20% then
the new dimensions are
Length = x ( 100-10)/100
= 90x /100
= 9x /10
Breadth = y x ( 100 +20 )/100
= 120y /100
= 12y /10
Perimeter = 240 cm
2 [ 9x /10 + 12y /10 ] = 240
9x + 12y = 1200
Divide each term with 3
3x + 4y = 400-----( 2 )
Multiply equation ( 1 ) with 3 and
Subtract from ( 2 )
y = 40
Put y = 40 in ( 1 )
x = 80
Therefore ,
Required rectangle dimensions are
Length = x = 80 cm
Breadth = y = 40 cm
This question is part of UPSC exam. View all Class 8 courses
Most Upvoted Answer
The perimeter of a rectangle is 240 CM if the length is decreased by 1...
The Problem:
The problem states that the perimeter of a rectangle is 240 cm. When the length of the rectangle is decreased by 10% and the breadth is increased by 20%, the new rectangle has the same perimeter. We need to find the length and breadth of the original rectangle.
Understanding the Problem:
To solve this problem, we need to understand the concept of perimeter and how it relates to the dimensions of a rectangle. The perimeter of a rectangle is the sum of all its sides. In this case, we are given that the perimeter is 240 cm.
Let's solve the problem step by step:
Step 1: Representing the dimensions of the rectangle:
Let's assume the original length of the rectangle is L and the original breadth is B. We are given that the perimeter of the rectangle is 240 cm.
Step 2: Calculating the initial perimeter:
The initial perimeter of the rectangle can be calculated using the formula: P = 2L + 2B, where P is the perimeter, L is the length, and B is the breadth.
Given that the perimeter is 240 cm, we have the equation: 2L + 2B = 240.
Step 3: Modifying the dimensions of the rectangle:
According to the problem, the length of the rectangle is decreased by 10% and the breadth is increased by 20%.
To decrease the length by 10%, we can multiply L by (100% - 10%) = 90% or 0.9.
To increase the breadth by 20%, we can multiply B by (100% + 20%) = 120% or 1.2.
So, the new length is 0.9L and the new breadth is 1.2B.
Step 4: Calculating the new perimeter:
The new perimeter of the modified rectangle can be calculated using the same formula: P = 2(0.9L) + 2(1.2B).
Since the new perimeter is equal to the original perimeter, we have the equation: 2(0.9L) + 2(1.2B) = 240.
Step 5: Solving the equation:
Let's solve the equation to find the values of L and B.
Expanding the equation, we get: 1.8L + 2.4B = 240.
Rearranging the terms, we have: 1.8L = 240 - 2.4B.
Dividing both sides by 1.8, we get: L = (240 - 2.4B)/1.8.
Step 6: Substituting the value of L:
Substituting the value of L in the equation 2L + 2B = 240, we get: 2((240 - 2.4B)/1.8) + 2B = 240.
Simplifying the equation, we have: (480 - 4.8B)/1.8 + 2B = 240.
Multiplying both sides by 1.8 to eliminate the denominator, we get: 480 - 4.8B + 3.6B = 432
The problem states that the perimeter of a rectangle is 240 cm. When the length of the rectangle is decreased by 10% and the breadth is increased by 20%, the new rectangle has the same perimeter. We need to find the length and breadth of the original rectangle.
Understanding the Problem:
To solve this problem, we need to understand the concept of perimeter and how it relates to the dimensions of a rectangle. The perimeter of a rectangle is the sum of all its sides. In this case, we are given that the perimeter is 240 cm.
Let's solve the problem step by step:
Step 1: Representing the dimensions of the rectangle:
Let's assume the original length of the rectangle is L and the original breadth is B. We are given that the perimeter of the rectangle is 240 cm.
Step 2: Calculating the initial perimeter:
The initial perimeter of the rectangle can be calculated using the formula: P = 2L + 2B, where P is the perimeter, L is the length, and B is the breadth.
Given that the perimeter is 240 cm, we have the equation: 2L + 2B = 240.
Step 3: Modifying the dimensions of the rectangle:
According to the problem, the length of the rectangle is decreased by 10% and the breadth is increased by 20%.
To decrease the length by 10%, we can multiply L by (100% - 10%) = 90% or 0.9.
To increase the breadth by 20%, we can multiply B by (100% + 20%) = 120% or 1.2.
So, the new length is 0.9L and the new breadth is 1.2B.
Step 4: Calculating the new perimeter:
The new perimeter of the modified rectangle can be calculated using the same formula: P = 2(0.9L) + 2(1.2B).
Since the new perimeter is equal to the original perimeter, we have the equation: 2(0.9L) + 2(1.2B) = 240.
Step 5: Solving the equation:
Let's solve the equation to find the values of L and B.
Expanding the equation, we get: 1.8L + 2.4B = 240.
Rearranging the terms, we have: 1.8L = 240 - 2.4B.
Dividing both sides by 1.8, we get: L = (240 - 2.4B)/1.8.
Step 6: Substituting the value of L:
Substituting the value of L in the equation 2L + 2B = 240, we get: 2((240 - 2.4B)/1.8) + 2B = 240.
Simplifying the equation, we have: (480 - 4.8B)/1.8 + 2B = 240.
Multiplying both sides by 1.8 to eliminate the denominator, we get: 480 - 4.8B + 3.6B = 432
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The perimeter of a rectangle is 240 CM if the length is decreased by 10% and the breadth is increased by 20% we get the same perimeter find the length and breadth of the rectangle?
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The perimeter of a rectangle is 240 CM if the length is decreased by 10% and the breadth is increased by 20% we get the same perimeter find the length and breadth 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 perimeter of a rectangle is 240 CM if the length is decreased by 10% and the breadth is increased by 20% we get the same perimeter find the length and breadth of the rectangle? covers all topics & solutions for Class 8 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The perimeter of a rectangle is 240 CM if the length is decreased by 10% and the breadth is increased by 20% we get the same perimeter find the length and breadth of the rectangle?.
The perimeter of a rectangle is 240 CM if the length is decreased by 10% and the breadth is increased by 20% we get the same perimeter find the length and breadth 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 perimeter of a rectangle is 240 CM if the length is decreased by 10% and the breadth is increased by 20% we get the same perimeter find the length and breadth of the rectangle? covers all topics & solutions for Class 8 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The perimeter of a rectangle is 240 CM if the length is decreased by 10% and the breadth is increased by 20% we get the same perimeter find the length and breadth of the rectangle?.
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