Exercise 121 Page 66

a To determine the big rectangle's area, we can either add the areas of the smaller rectangles that are inside of the bigger rectangle, or we can multiply the length of the bigger rectangle's vertical and horizontal sides. From the diagram we can determine the length of the vertical and horizontal side.

If we multiply the length of the area model's vertical and horizontal sides, we can create an expression that describes the area. As a product (x+6)(3x+(-2)) ⇕ (x+6)(3x-2) To determine the area of the smaller rectangles, we have to multiply their respective horizontal and vertical sides.

Let's perform the multiplications.

By adding the area of the smaller rectangles, we can obtain an expression for the bigger rectangles area. As a sum 18x+3x^2+(-12)+(-2x) ⇕ 3x^2+16x-12

b Like in Part A, we will begin by finding an expression for the area as a product.

If we multiply the length of the area model's vertical and horizontal side, we can create an expression that describes the area. As a product (2y+(-7))(6y+(-4)) ⇕ (2y-7)(6y-4) To determine the area of the smaller rectangles, we have to multiply their respective horizontal and vertical sides.

Let's perform the multiplications.

By adding the area of the smaller rectangles, we can obtain an expression for the bigger rectangle's area. As a sum -42x+12y^2+28+(-8y) ⇕ 12y^2-50y+28

c The area of a rectangle is the product of its width and length. In both exercises, we know these dimensions since we know the length of the bigger rectangle's sides.

Subchapter links

Exercises

116

117

118

119

120

121

122

Exercise 121 Page 66

Hints

Check the answer