Question

The length of a throw pillow is 64 centimeter longer than its width and the area is 110 cm². Is it a quadratic or not?

Option 1: Yes, it's a quadratic.
Option 2: No, it's not a quadratic.

Answer 1

The relationship of the dimensions of a throw pillow with its given area forms a quadratic equation because it includes a w^2 term, confirming that it is Option 1: Yes, it's a quadratic.

Step-by-step explanation:

Considering the dimensions of a throw pillow where its length is 64 centimeters longer than its width and the area is 110 cm², we can set up an equation to represent this relationship. Let w be the width of the pillow. Then the length is w + 64 cm. We know that area is calculated by multiplying the length by the width, so:

Area = length × width

110 cm² = (w + 64) × w

This is a quadratic equation because when you expand the equation, you get:

w² + 64w - 110 = 0

Since there is a w² term, it is indeed a quadratic. Therefore, the correct answer is Option 1: Yes, it's a quadratic.