The percentage increase in the area of a rectangle if each of its sides is increased by 20% is

1. 32%
2. 34%
3. 42%
4. 44%

Solution

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Correct option is D. 44%

Let the original length of the rectangle be L and the original width be W.

When each side is increased by 20%, the new length becomes 1.20L (which is L + 0.20L) and the new width becomes 1.20W (which is W + 0.20W).

The original area (A1) of the rectangle is given by: A1 = L * W

The new area (A2) of the rectangle after the increase is given by: A2 = 1.20L * 1.20W = 1.44LW

Now, we need to find the percentage increase in the area. The increase in area (ΔA) is the difference between the new area (A2) and the original area (A1):

ΔA = A2 – A1 ΔA = 1.44LW – LW ΔA = 0.44LW

To find the percentage increase in the area, we divide the increase in area (ΔA) by the original area (A1) and multiply by 100:

Percentage increase = (ΔA / A1) * 100 Percentage increase = (0.44LW / LW) * 100

Since LW appears both in the numerator and the denominator, we can cancel it out:

Percentage increase = 0.44 * 100 Percentage increase = 44%

So, the area of the rectangle increases by 44% when each of its sides is increased by 20%.