The lengths of the sides of a rectangle become 4 times greater than the original measurements. Which statement is true about the rectangle?

A. Its area becomes 4 times greater, and perimeter becomes 16 times greater.
B. Its area becomes 16 times greater, and perimeter becomes 4 times greater.
C. Its area becomes 20 times greater, and perimeter becomes 4 times greater.
D. Its area becomes 4 times greater, and perimeter becomes 20 times greater.

To determine the correct answer, let's first analyze the effect of multiplying the lengths of the sides of a rectangle by 4.

1. Area: The area of a rectangle is given by the formula A = length * width. If both the length and width are multiplied by 4, the new area will be (4 * length) * (4 * width) = 16 * (length * width). Therefore, the area becomes 16 times greater.

2. Perimeter: The perimeter of a rectangle is given by the formula P = 2 * (length + width). If both the length and width are multiplied by 4, the new perimeter will be 2 * ((4 * length) + (4 * width)) = 2 * (4 * (length + width)). Therefore, the perimeter becomes 4 times greater.

Based on this analysis, we can conclude that option B is correct: The area becomes 16 times greater, and the perimeter becomes 4 times greater.