The perimeter of a rectangular baking sheet is 58 inches and its area is 201.25 in.2. what are the length and width of the baking sheet?

The length and width of the baking sheet are 17.5 inches and 11.5 inches respectively.

The perimeter of a rectangle is given as: 2l + 2w

The area of a rectangle is given as l×w

2l + 2w = 58

l + w = 29 equation i

l × w = 201.25 equation ii

From equation i, l = 29 - w

Since l×w = 201.25

(29 - w)w = 201.25

w² - 29w = 201.25

w² - 29w - 201.25 = 0

w² - 17.5w - 11.5w - 201.25 = 0

w(w - 17.5) - 11.5(w - 17.5)

(w - 17.5) = 0 and (w - 11.5) = 0

w - 11.5 = 0

w = 0 + 11.5 = 11.5

Width = 11.5 inches

Length = 17.5 inches

Therefore, the length and width of the baking sheet are 17.5 inches and 11.5 inches respectively.

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Step-by-step explanation:

The formula for calculate the Area of a rectangle is:

Where "l" is the lenght and "w" is the width.

And the formula for calculate the peimeter of a rectangle is:

Where "l" is the lenght and "w" is the width.

We know that the perimeter of the rectangular baking sheet is 58 inches and its area is 201.25 in². Then:

The steps are:

1. Solve for the "l" from the formula :

2. Substitute into the formula and solve for "w":

Applying the Quadratic formula , we get:

3.  Substitute into :

4. Substitute into :

Therefore, since the value of the lenght of a rectangle must be greater that the value of the width, we can conclude that the lenght and the width of the rectangular baking sheet are:

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∈3,600

step-by-step explanation: