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The percentage increase in the area of a rectangle, if each of its sides is increased by 20%, is:
- a)40%
- b)42%
- c)44%
- d)46%
Correct answer is option 'C'. Can you explain this answer?
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Verified Answer
The percentage increase in the area of a rectangle, if each of its sid...
Let original length = x metres and original breadth = y metres.
Original area = (xy) m2.
New length = (120/100) × m = (6/5) × m
New breadth = (120/100) y m = (6/5) y m
New area = (6/5) × m × (6/5) y m
= (36/25)xy m2
The difference between the original area
= xy and new area 36/25 xy is
= (36/25)xy – xy
= xy( 36/25 – 1)
= xy( 11/25) or (11/25)xy
∴ Increase %
= [(11/25)xy × 1/xy × 100]%
= 44%
Original area = (xy) m2.
New length = (120/100) × m = (6/5) × m
New breadth = (120/100) y m = (6/5) y m
New area = (6/5) × m × (6/5) y m
= (36/25)xy m2
The difference between the original area
= xy and new area 36/25 xy is
= (36/25)xy – xy
= xy( 36/25 – 1)
= xy( 11/25) or (11/25)xy
∴ Increase %
= [(11/25)xy × 1/xy × 100]%
= 44%
Most Upvoted Answer
The percentage increase in the area of a rectangle, if each of its sid...
Explanation:
To find the percentage increase in the area of a rectangle, we need to calculate the new area of the rectangle after increasing each of its sides by 20%.
Let's assume the length of the rectangle is L and the width is W.
Step 1:
We know that the area of a rectangle is given by the formula: Area = Length × Width.
So, the original area of the rectangle is: Area1 = L × W.
Step 2:
If each side of the rectangle is increased by 20%, the new length will be (L + 0.2L) = 1.2L and the new width will be (W + 0.2W) = 1.2W.
Step 3:
Now, we can calculate the new area of the rectangle using the formula: Area2 = (1.2L) × (1.2W) = 1.44LW.
Step 4:
To find the percentage increase in the area, we need to calculate the difference between the new area and the original area, and then express it as a percentage of the original area.
The difference in the areas is: Area2 - Area1 = 1.44LW - LW = 0.44LW.
Step 5:
We can express this increase as a percentage of the original area by dividing the difference by the original area and multiplying by 100.
Percentage increase = (0.44LW / LW) × 100 = 44%.
Therefore, the percentage increase in the area of the rectangle is 44%, which corresponds to option C.
To find the percentage increase in the area of a rectangle, we need to calculate the new area of the rectangle after increasing each of its sides by 20%.
Let's assume the length of the rectangle is L and the width is W.
Step 1:
We know that the area of a rectangle is given by the formula: Area = Length × Width.
So, the original area of the rectangle is: Area1 = L × W.
Step 2:
If each side of the rectangle is increased by 20%, the new length will be (L + 0.2L) = 1.2L and the new width will be (W + 0.2W) = 1.2W.
Step 3:
Now, we can calculate the new area of the rectangle using the formula: Area2 = (1.2L) × (1.2W) = 1.44LW.
Step 4:
To find the percentage increase in the area, we need to calculate the difference between the new area and the original area, and then express it as a percentage of the original area.
The difference in the areas is: Area2 - Area1 = 1.44LW - LW = 0.44LW.
Step 5:
We can express this increase as a percentage of the original area by dividing the difference by the original area and multiplying by 100.
Percentage increase = (0.44LW / LW) × 100 = 44%.
Therefore, the percentage increase in the area of the rectangle is 44%, which corresponds to option C.
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