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the length of a rectangular field is increased by 50%and it's breadth is decreased by 50%to form a new rectangular field. find the percentage change in the area of the field.
Verified Answer
the length of a rectangular field is increased by 50%and it's breadth ...
Let length of rectangle is L
breadth of rectangle is B
area of rectangle = LB
a/c to question,
length increased by 50% e.g., new length of rectangle is L + L/2 = 3L/2
breadth decreased by 50% e.g., new breadth of reactangle is B - B/2 = B/2
now, new area of rectangle is 3L/2 * B/2 = 3LB/4
hence, % change in area = ( final area - initial area )/initial area * 100
= (3LB/4 -LB)/LB *100 = -25%
here negative sign shows area decreased by 25 %
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the length of a rectangular field is increased by 50%and it's breadth ...
Problem:
The length of a rectangular field is increased by 50% and its breadth is decreased by 50% to form a new rectangular field. Find the percentage change in the area of the field.
Solution:
Step 1: Understanding the Problem
Let's assume the original length of the rectangular field is L and the original breadth is B. We need to find the percentage change in the area of the field when the length is increased by 50% and the breadth is decreased by 50%.
Step 2: Calculating the New Length and Breadth
When the length is increased by 50%, the new length becomes L + (50/100)L = 1.5L.
When the breadth is decreased by 50%, the new breadth becomes B - (50/100)B = 0.5B.
Step 3: Calculating the New Area
The area of the original rectangular field is A = L * B.
The area of the new rectangular field is A' = (1.5L) * (0.5B) = 0.75LB.
Step 4: Calculating the Percentage Change
The percentage change in the area can be calculated using the formula:
Percentage Change = ((New Value - Old Value) / Old Value) * 100
In this case, the old value is A and the new value is A'.
So, the percentage change in the area is:
Percentage Change = ((0.75LB - LB) / LB) * 100
= (-0.25LB / LB) * 100
= -25%
Step 5: Final Answer
The percentage change in the area of the field is -25%.
Conclusion:
The area of the rectangular field decreases by 25% when the length is increased by 50% and the breadth is decreased by 50%.
The length of a rectangular field is increased by 50% and its breadth is decreased by 50% to form a new rectangular field. Find the percentage change in the area of the field.
Solution:
Step 1: Understanding the Problem
Let's assume the original length of the rectangular field is L and the original breadth is B. We need to find the percentage change in the area of the field when the length is increased by 50% and the breadth is decreased by 50%.
Step 2: Calculating the New Length and Breadth
When the length is increased by 50%, the new length becomes L + (50/100)L = 1.5L.
When the breadth is decreased by 50%, the new breadth becomes B - (50/100)B = 0.5B.
Step 3: Calculating the New Area
The area of the original rectangular field is A = L * B.
The area of the new rectangular field is A' = (1.5L) * (0.5B) = 0.75LB.
Step 4: Calculating the Percentage Change
The percentage change in the area can be calculated using the formula:
Percentage Change = ((New Value - Old Value) / Old Value) * 100
In this case, the old value is A and the new value is A'.
So, the percentage change in the area is:
Percentage Change = ((0.75LB - LB) / LB) * 100
= (-0.25LB / LB) * 100
= -25%
Step 5: Final Answer
The percentage change in the area of the field is -25%.
Conclusion:
The area of the rectangular field decreases by 25% when the length is increased by 50% and the breadth is decreased by 50%.
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the length of a rectangular field is increased by 50%and it's breadth is decreased by 50%to form a new rectangular field. find the percentage change in the area of the field. Related: Short Notes - Mensuration, Mathematics Class 8th
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