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.
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
1 answer