JAMB - Mathematics (1987 - No. 6)
If the length of a square is increased by 20% while 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?
6 : 5
25 : 24
5 : 6
24 : 25
Explanation
Length and width of a square is 100%
Length increased by 20% and
Width decreased by 20% to form a rectangle
Length of rectangle = 120% to form a rectangle
Length of rectangle = 120% and
Width of rectangle = 80%
Area of rectangle = L x W
Area of square = W
Ratio of the area of the rectangle to the area of the square
A = \(\frac{\text{Area of rectangle}}{\text{Area of square}}\)
\(\frac{120 \times 30}{100 \times 100}\) = \(\frac{96}{100}\)
= 24 : 25
Length increased by 20% and
Width decreased by 20% to form a rectangle
Length of rectangle = 120% to form a rectangle
Length of rectangle = 120% and
Width of rectangle = 80%
Area of rectangle = L x W
Area of square = W
Ratio of the area of the rectangle to the area of the square
A = \(\frac{\text{Area of rectangle}}{\text{Area of square}}\)
\(\frac{120 \times 30}{100 \times 100}\) = \(\frac{96}{100}\)
= 24 : 25
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