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kiyagibbskg
 To minimize the perimeter you should always have a square. 
sqrt(289) = 17 
The dimensions should be 17 X 17 

To see , try starting at length 1, and gradually increase the length. 
The height decreases at a faster rate than the length increases, up until you reach a square. 

Or if you want to use algebra, Say the width is 17-x 
Then the length is 289/(17-x) 

Now, this is bigger than 17+x, as shown here: 
289/(17-x) > 17+x 
289 > 289 - x^2 
which is true. 
so the perimeter would be bigger than 2 * (17- x + 17 + x) = 2 * (2 * 17) = 4 * 17 

Again, the dimensions should be a square. 17 X 17.
raphealnwobi

The minimum perimeter of the rectangle with an area of 289 square inches is 68 inches.

Let x represent the length of the rectangle and y represent the width of the rectangle.

Since the area is  289 square inches, hence:

xy = 289

y = 289/x

The perimeter of the rectangle is:

Perimeter (P) = 2(x + y)

P = 2(x + 289/x)

P = 2x + 578/x

The minimum perimeter is at P' = 0, hence:

P' = 2 - 578/x² = 0

578/x² = 2

2x² = 578

x = 17 inches

y = 289 / x = 289 / 17 = 17 inches

Perimeter = 2(x + y) = 2(17 + 17) = 68

The minimum perimeter of the rectangle with an area of 289 square inches is 68 inches.

Find out more at: https://brainly.com/question/23581229

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