A gardener increased the area of his rectangular garden by increasing its length by 40% and decreasing its wid

Question

A gardener increased the area of his rectangular garden by increasing its length by 40% and decreasing its width by 20%. The area of the new garden

Accepted Answer

Let the original length of the rectangular garden be L and its original width be W.
The original area of the garden = L * W.

The length is increased by 40%.
New length = L + 0.40L = 1.40L.

The width is decreased by 20%.
New width = W - 0.20W = 0.80W.

The new area of the garden = (New length) * (New width)
New area = (1.40L) * (0.80W)
New area = (1.40 * 0.80) * (L * W)
New area = 1.12 * (L * W)

Since the original area was L * W, the new area is 1.12 times the original area.
This means the new area is 112% of the original area.
The percentage increase in area = (New Area - Original Area) / Original Area * 100
= (1.12 * Original Area - Original Area) / Original Area * 100
= (0.12 * Original Area) / Original Area * 100
= 0.12 * 100 = 12%.

Therefore, the area of the new garden has increased by 12%.

Option A is incorrect because the calculation shows a 12% increase, not 20%.
Option B is correct as the new area is 1.12 times the old area, representing a 12% increase.
Option C is incorrect as the increase is 12%, not 8%.
Option D is incorrect as the new area is clearly greater than the old area (1.12 > 1).

The final answer is B

Answer

has increased by 20%

Answer

has increased by 12%

Answer

has increased by 8%

Answer

is exactly the same as the old area.

A gardener increased the area of his rectangular garden by increasing its length by 40% and decreasing its width by 20%. The area of the new garden

Explanation

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