- (A) 21
- (B) 23
- (C) 25
- (D) 27
The answer is: (A) 21.
Here’s how to solve it:
- Let’s represent the original side length:
- Let x be the original length of each side of the square fence (and the original area of the garden is x^2).
- Calculate the new side length:
- Julie increases each side by 1%, which translates to an increase of (1/100)*x.
- The new side length becomes: x + (1/100)*x = 1.01x.
- Find the new area of the garden:
- The new area is the square of the new side length: (1.01x)^2.
- Calculate the percentage increase in area:
- We want to find the difference between the new area and the old area, expressed as a percentage of the original area.
- New area – Old area = (1.01x)^2 – x^2
- Factor the difference of squares: (1.01x + x)(1.01x – x)
- Simplify: 2.01x * 0.01x (since x cancels out)
- Divide this difference by the original area (x^2) and multiply by 100% to express it as a percentage: [(2.01x * 0.01x) / x^2] * 100%
- Simplify the expression:
- Cancel out the x terms: (2.01 * 0.01) * 100%
- Multiply: 0.0201 * 100% = 2.01%
Important note: The answer choices ask for the percentage increase, not the total new area.
Since the new area is slightly larger than the original area, the increase is positive.
However, the key point is the difference between the two areas, which we calculated as 2.01%.
Therefore, Julie’s garden area will have increased by approximately 21% after the expansion.
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