Question

A steel company is making flat rectangular frames as a part of a new product they are launching. Each frame will be cut out of a piece of steel and will have a final area as close to 28 cm² as possible. The width of the frame needs to be uniform throughout. The inside dimensions of the frame must be 11 cm by 6 cm. Complete the equation that models the above situation, and find the width of the frame, x. The area of the steel frame can be modeled by the following equation.

a) x² + 5x - 28 = 0

b) x² - 5x - 28 = 0

c) x² + 6x - 28 = 0

d) x² - 6x - 28 = 0

Answer 1

The equation that models the situation is d) x² - 6x - 28 = 0. The width of the frame is 7 cm.

Step-by-step explanation:

The equation that models the situation is d) x² - 6x - 28 = 0. To find the width of the frame, we need to solve this equation.

We can factorize the equation as (x-7)(x+4) = 0.

So, x = 7 or x = -4. Since the width cannot be negative, the width of the frame is 7 cm.