Question

A steel company is making flat rectangular frames as a part of a new product. 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 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+11x−28=0

b. x2−11x−28=0

c. x2+11x+28=0

d. x2−11x+28=0

The width of the frame, x, rounded to the nearest hundredth, is approximately ___ cm.

Answer 1

The equation that models the situation is x^2 - 11x + 28 = 0. The width of the frame is approximately 4 cm.

Step-by-step explanation:

The equation that models the situation described is: x^2 - 11x + 28 = 0. To find the width of the frame, we need to solve this equation. By factoring or using the quadratic formula, we find the solutions to be x = 4 and x = 7. Since the width of the frame cannot be negative, the width of the frame is approximately 4 cm.