Final answer:
The relationship between the dimensions of the pillow and its area is quadratic, as the equation for the area is w(w + 64) = 110 cm², which is a quadratic equation. The correct answer is A) Yes, it is a quadratic relationship, exemplified by how dimensions scale with the area of geometric shapes.
Step-by-step explanation:
The relationship between the dimensions of the pillow and its area is indeed a quadratic relationship. If we let w represent the width of the pillow, then the length of the pillow would be w + 64 centimeters. The area of a rectangle (which is the shape of the pillow) is calculated by multiplying its length by its width, which in this case gives us the equation:
Area = w × (w + 64)
If we know the area is 110 cm², we can set up the equation 110 = w × (w + 64), which is a quadratic equation because it can be rewritten as w² + 64w - 110 = 0.
Therefore, the correct answer is A) Yes, it is a quadratic relationship.
Comparing this to examples of area scaling in geometry, like Marta's squares, helps demonstrate how properties, such as area, change in relation to the dimensions of a shape. When the dimensions of Marta's square are doubled (from 4 inches to 8 inches), the area is multiplied by the square of that scale factor (2² = 4), meaning the area of the larger square is four times the area of the smaller square.