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If the length of a rectangular field is increased by 20% and the breadth is reduced by 20%, the area of the rectangle will be 192m². What is the area of original rectangle?
- a)100m²
- b)150m²
- c)175m²
- d)200m²
- e)None of the Above
Correct answer is option 'D'. Can you explain this answer?
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Verified Answer
If the length of a rectangular field is increased by 20% and the bread...
length of rectangle = l m
breadth of rectangle = b m
l * (120/100) * b * (80/100) = 192
1.2l * 0.8b = 192
lb = 192 / 1.2 * 0.8 = 200 m²
breadth of rectangle = b m
l * (120/100) * b * (80/100) = 192
1.2l * 0.8b = 192
lb = 192 / 1.2 * 0.8 = 200 m²
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If the length of a rectangular field is increased by 20% and the bread...
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If the length of a rectangular field is increased by 20% and the bread...
Let's assume the original length of the rectangular field is L and the original breadth is B.
The area of the rectangle is given by A = L * B.
When the length is increased by 20%, the new length becomes L + 0.2L = 1.2L.
When the breadth is reduced by 20%, the new breadth becomes B - 0.2B = 0.8B.
The new area of the rectangle is (1.2L) * (0.8B) = 0.96LB.
Given that the new area is 192m², we have 0.96LB = 192.
Dividing both sides of the equation by 0.96, we get LB = 200.
Therefore, the original area of the rectangle is 200m².
The area of the rectangle is given by A = L * B.
When the length is increased by 20%, the new length becomes L + 0.2L = 1.2L.
When the breadth is reduced by 20%, the new breadth becomes B - 0.2B = 0.8B.
The new area of the rectangle is (1.2L) * (0.8B) = 0.96LB.
Given that the new area is 192m², we have 0.96LB = 192.
Dividing both sides of the equation by 0.96, we get LB = 200.
Therefore, the original area of the rectangle is 200m².
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