Question

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?

Answer 1

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:

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

The steps are:

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:

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

Answer 2

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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