Question

Janis is the set designer for a play. She has 40 feet of dividers to use to create a section in the workshop for storing props. She

plans to create the space in the corner of the workshop and use the dividers to create the extra two walls. The area of the sectioned off space, A, is modeled by this equation, where x is the width of the prop section.
A = -12 + 402, Which equation reveals the dimensions that will create the maximum area of the prop section?
A) A = -(t – 400)
B) A = -(– 20)2 + 400
C) A = -(x – 20) (1 - 20)
D) A = -2(x - 40).

Answer 1

The equation that reveals the dimensions that will create the maximum area of the prop section is A = -(x - 20)(40 - x). The dimensions that will create the maximum area are a width of 20 feet and a length of 20 feet.

Step-by-step explanation:

The equation that reveals the dimensions that will create the maximum area of the prop section is A = -(x - 20)(40 - x).

To find the dimensions that will create the maximum area, we need to maximize the equation A = -(x - 20)(40 - x).

We can do this by finding the x-value that corresponds to the maximum point on the graph of this equation. We can use a graphing calculator or algebraic methods such as completing the square or finding the vertex of a quadratic equation to find that the maximum area occurs when x = 20. Therefore, the dimensions that will create the maximum area of the prop section are a width of 20 feet and a length of (40 - 20) = 20 feet.