Question

An office wants to create a cubicle for a new employee. The cubicle will be rectangular​ , with three sides enclosed by cubicle wall and the fourth side open. What dimensions should be used to get the largest possible cubicle if the office has 300 feet of cubicle​ wall? Part 1 The length of the shorter side is enter your response here feet.

The length of the longer side is enter your response here feet

Answer 1

To create the largest possible cubicle with 300 feet of cubicle wall, the shorter side should be 60 feet long and the longer side should be 120 feet long.

Step-by-step explanation:

To get the largest possible cubicle with 300 feet of cubicle wall, we can use a rectangle with three sides enclosed by cubicle walls and one side open. Let's assume the shorter side of the cubicle is x feet long.

The longer side will be twice the length of the shorter side, so it will be 2x feet long.

The total length of the cubicle wall is the sum of the lengths of the four sides, which is 300 feet.
Therefore, we have the equation: x + x + 2x + x = 300.

Simplifying the equation, we get: 5x = 300.
Dividing both sides by 5, we find: x = 60.

So, the length of the shorter side is 60 feet and the length of the longer side is 2(60) = 120 feet.

Answer 2

To create the largest cubicle using 300 feet of wall, given three sides enclosed, the optimal dimensions are a length (shorter side) of 112.5 feet and a width (longer side) of 75 feet.

Step-by-step explanation:

To determine the dimensions for the largest possible cubicle with 300 feet of cubicle wall, we need to maximize the area of the rectangular cubicle with three walls, since one side is open. The perimeter of the cubicle with three sides can be represented as P = 2l + w, where l is the length of the longer side, w is the length of the shorter side (the width), and the total available wall material is P = 300 feet. We want to maximize the area A = l * w. Using the perimeter formula, we can express the width in terms of the length: w = 300 - 2l. Substituting this into the area formula, we get A = l * (300 - 2l) = 300l - 2l^2.

To find the maximum area, we can take the derivative of A with respect to l, set it equal to zero, and solve for l. dA/dl = 300 - 4l = 0, so l = 75 feet. Plugging this back into the expression for w gives w = 300 - 2*75 = 150 feet. However, since the cubicle has only three sides, we need to calculate the width by dividing the remaining wall material by two. Thus, the width is actually w = (300 - 75) / 2 = 112.5 feet.

Hence, for the largest possible cubicle, the length of the shorter side is 112.5 feet, and the length of the longer side is 75 feet.