Questions: In the figure shown, the center square is removed. a. Divide the remaining figure into two rectangles. What are the dimensions of each rectangle? b. What is the area of each rectangle? c. What is the total area of the remaining figure? How does this figure represent the difference of two squares? a. Determine the dimensions of each rectangle. Select all that apply A. (x-y) by (x-y) B. y by (x-y) C. x by y D. x by (x-y)

Solution Steps

We can divide the L-shaped remaining figure into two rectangles by extending the line of the smaller square's top edge to meet the larger square's left-hand edge. This creates a rectangle with dimensions _x_ by (_x_ - _y_) and a smaller rectangle below it with dimensions _y_ by (_x_ - _y_).

Rectangle 1: _x_ by (_x - y_) Rectangle 2: _y_ by (_x - y_) Therefore, the correct options are B and D.

Area of Rectangle 1: _x_(_x - y_) = _x_² - _xy_ Area of Rectangle 2: _y_(_x - y_) = _xy_ - _y_²

Total area: (_x_² - _xy_) + (_xy_ - _y_²) = _x_² - _y_²

This represents the difference of two squares (the larger square’s area, _x_², minus the smaller square’s area, _y_²).

Final Answer