Find the dimensions of a rectangle with a fixed area of 50 square units that min

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Question: Find the dimensions of a rectangle with a fixed area of 50 square units that minimizes the perimeter. (2020)

Options:

Correct Answer: 7, 7

Exam Year: 2020

Solution:

For a fixed area, the perimeter is minimized when the rectangle is a square. Thus, side = √50.

Find the dimensions of a rectangle with a fixed area of 50 square units that minimizes the perimeter. (2020)

Find the dimensions of a rectangle with a fixed area of 50 square units that minimizes the perimeter. (2020)

Step 1: Understand that we need to find the dimensions of a rectangle with an area of 50 square units.
Step 2: Recall the formula for the area of a rectangle, which is length times width (Area = length × width).
Step 3: Set up the equation for the area: length × width = 50.
Step 4: To minimize the perimeter, remember that the perimeter of a rectangle is given by the formula P = 2(length + width).
Step 5: To minimize the perimeter for a fixed area, we can use the fact that a square has the smallest perimeter for a given area.
Step 6: Since the area is 50, we can find the side length of the square by taking the square root of the area: side = √50.
Step 7: Therefore, the dimensions of the rectangle that minimize the perimeter are both equal to √50.

Optimization – The problem involves finding the dimensions of a rectangle that minimize the perimeter while maintaining a fixed area.
Geometric Properties – Understanding the relationship between area and perimeter in geometric shapes, particularly rectangles and squares.