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AnnyKZ [126]
3 years ago
15

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 bakin

g sheet?
Mathematics
1 answer:
anzhelika [568]3 years ago
8 0

Answer:

Length=17.5\ in\\\\Width=11.5\ in

Step-by-step explanation:

The formula for calculate the Area of a rectangle is:

A=lw

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

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

P=2l+2w

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:

A=201.25\ in^2\\\\P=58\ in

<u>The steps are:</u>

1. Solve for the "l" from the formula A=lw:

A=lw\\\\l=\frac{A}{w}\\\\\l=\frac{201.25}{w}

2. Substitute l=\frac{201.25}{w} into the formula P=2l+2w and solve for "w":

58=2(\frac{201.25}{w})+2w\\\\58=\frac{402.5}{w}+2w\\\\58=\frac{402.5+2w^2}{w}\\\\58w=402.5+2w^2\\\\2w^2-58w+402.5=0

Applying the Quadratic formula x=\frac{-b\±\sqrt{b^2-4ac}}{2a}, we get:

x=w=\frac{-(-58)\±\sqrt{(-58)^2-4(2)(402.5)}}{2(2)}\\\\w_1=17.5\\\\w_2=11.5

3.  Substitute w_1=17.5 into l=\frac{201.25}{w}:

l=\frac{201.25}{17.5}=11.5

4. Substitute w_2=11.5 into l=\frac{201.25}{w}:

l=\frac{201.25}{11.5}=17.5

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:

l=17.5\ in\\\\w=11.5\ in

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