Final answer:
The correct equation to describe the relationship between the areas of the square and the rectangle, where the rectangle's length is 5 more than the square's side and width is half the square's side, is (x + 5) * (x / 2) = x². The correct answer is a. (x + 5) * (x / 2) = x².
Step-by-step explanation:
A student is interested in finding out the dimensions of a square and comparing it to a rectangle, whose length is 5 units more than the square's side, and width is half the side of the square. The question seeks an equation to describe the situation, given that the areas of the square and the rectangle are equal.
The side length of the square is represented by x. The area of the square can be expressed as x². The length of the rectangle is x + 5, and its width is x / 2. The area of the rectangle is therefore (x + 5) * (x / 2). Setting the two areas equal to each other gives us the equation:
(x + 5) * (x / 2) = x², which is the equation describing the situation where both the square and rectangle have the same area.
To compare the areas of two squares where one square has dimensions that are twice that of the first square, we would say the side length of the larger square is 4 inches x 2 = 8 inches.
Thus, the area of the larger square, being the square of its side length, would be 8 inches², which is 64 square inches, and this area is four times larger than the area of the smaller square with a side length of 4 inches.