Answer: To sketch all the possible rectangles that Kay could make with 16 small squares and 1 large square, we can arrange them in different configurations. For example:
One possible rectangle could have a length of 8 small squares and a width of 2 small squares. The large square would be used to fill in the empty space at one end of the rectangle.
8 small squares
8 small squares
1 large square
The area of this rectangle is (8)(2) + 1 = 17. We can write this in standard form as 17 and in factored form as 17 = 17(1).
Another possible rectangle could have a length of 4 small squares and a width of 4 small squares. The large square would be used to fill in the empty space at one end of the rectangle.
4 small squares 4 small squares
4 small squares 4 small squares
1 large square
The area of this rectangle is (4)(4) + 1 = 17. We can write this in standard form as 17 and in factored form as 17 = 1(17).
A third possible rectangle could have a length of 8 small squares and a width of 1 small square. The large square would be used to fill in the empty space at one end of the rectangle.
8 small squares
1 large square
The area of this rectangle is (8)(1) + 1 = 9. We can write this in standard form as 9 and in factored form as 9 = 9(1).
A fourth possible rectangle could have a length of 4 small squares and a width of 2 small squares. The large square would be used to fill in the empty space at one end of the rectangle.
4 small squares 2 small squares
4 small squares 2 small squares
1 large square
The area of this rectangle is (4)(2) + 1 = 9. We can write this in standard form as 9 and in factored form as 9 = 3(3).
So, there are four possible rectangles that Kay could make with 16 small squares and 1 large square, and the area of each rectangle can be expressed in both standard form and factored form as shown above.
Explanation: