Answer :
The maximum length or width we can increase so that it will not exceed the capacity of AC is 100 feet.
What is rectangle?
An enclosed 2-D shape called a rectangle has four sides, four corners, and four right angles (90°). A rectangle has equal and parallel, opposite sides. Since a rectangle is a two-dimensional form, it has two dimensions: length and width. The rectangle's longer side is its length, while its shorter side is its breadth.
Given:
The volume AC can cool, v = 40000 feet³,
The dimensions of the room are 75 feet × 50 feet × 8 feet.,
Calculate the volume of the room as shown below,
Volume = 75 feet × 50 feet × 8 feet
Volume = 30000 feet³
The remaining margin of volume = 40000 - 30000
The remaining margin of volume = 10000 feet³
Thus, the maximum dimension we can increase in length and width is 100 feet.
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Final answer:
The length and the width of the room can be increased by approximately 7.4 feet without exceeding the air conditioning's capacity of 40,000 cubic feet.
Explanation:
Firstly, we need to understand that we need to find the increment that can be made to the length and the width of the room without exceeding the air conditioner's capacity of 40,000 cubic feet. Let's denote the increment as 'x'. So, the increased length and width will be 75 + x and 50 + x, respectively. The height remains 8 feet.
Since the volume of a rectangular room is given by length * width * height, the volume of the increased room will be (75 + x) * (50 + x) * 8. Setting this = 40,000, we can create the following equation:
8(75 + x)(50 + x) = 40000
By simplifying the above equation we get x^2 + 125x - 6250 = 0. By solving this equation for 'x', we get approximately x = 7.4 feet when rounded to the nearest tenth which means a 7.4 feet increase in both length and width would not exceed the capacity of the air conditioner.
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