If the length of a square is
increased by 20% while its width
is decreased by 20% to form a
rectangle, what is the ratio of the
area of the rectangle to the area
of the square?
A. 6:5
B. 23:24
C. 5:6
D. 24:25
Let the original side length of the square be x.
After increasing the length by 20%, the new length becomes 1.2x.
After decreasing the width by 20%, the new width becomes 0.8x.
The area of the rectangle is the product of its length and width, so the area of the rectangle is (1.2x)(0.8x) = 0.96x^2.
The area of the square is x^2.
The ratio of the area of the rectangle to the area of the square is therefore (0.96x^2)/(x^2) = 0.96.
To simplify the ratio, we can multiply both the numerator and denominator by 100 to remove the decimal point.
The ratio becomes 96/100 = 24/25.
Therefore, the answer is D. 24:25.
To find the ratio of the area of the rectangle to the area of the square, we first need to calculate the areas of both shapes.
Let's assume the original length of the square is L and the original width is W.
The area of the square is given by A_square = L * W.
According to the problem, the length of the square is increased by 20%. This means the new length of the rectangle is L + 0.2L = 1.2L.
On the other hand, the width is decreased by 20%. This means the new width of the rectangle is W - 0.2W = 0.8W.
The area of the rectangle can be calculated as A_rectangle = (1.2L) * (0.8W) = 0.96LW.
Now, we can find the ratio of the area of the rectangle to the area of the square:
Ratio = A_rectangle / A_square
Ratio = (0.96LW) / (LW)
Ratio = 0.96/1
Ratio = 0.96
Therefore, the ratio of the area of the rectangle to the area of the square is 0.96:1, which simplifies to 24:25.
Hence, the correct answer is option D. 24:25.