What is x if the area of a rectangle is 16 and the length of the rectangle is x^5/(x+1) and the width is (x+1)/x^3?

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hala718's profile pic

hala718 | High School Teacher | (Level 1) Educator Emeritus

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given a rectangle with length (L) and width (W)

L = (x^5)/(x+1)

W = (x+1)/x^3

Also given that the area of the rectangle = 16

But the area A is:

A = L *w = 16

==> (x^5)/(x+1) * (x+1)/x^3 = 16

Reduce similar terms:

==> x^5/ x^3 = 16

But we know that: x^a/x^b = x^(a-b):

==> x^(4-3) = 16

==> x^2 = 16

==> x= 4

Now to find the sides of the rectangle, we will substitue with x= 4:

L = x^5/(x+1) = 4^5/(5) = 1024/5 = 204.8

W = (x+1)/x^3 = 5/4^3 = 5/64= 0.078125

==> L *W = 204.8 * 0.078125 = 16

neela's profile pic

neela | High School Teacher | (Level 3) Valedictorian

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The product of the length and width is the area of the rectangle.

Length = x^5/(x+1) , width = (x+1)/x^3. Area = 16.

Therefore  length*width = area.

(x^5/(x+1)}*{(x+1)/x^3 } = 16

x+1 gets cacelled .

x^5/x^3 = 16

x^2 = 16.

x  = sqrt16

x = 4.

giorgiana1976's profile pic

giorgiana1976 | College Teacher | (Level 3) Valedictorian

Posted on

The area of a rectangle is the product of width and length.

A = w*l

From enunciation, we know that the length of the rectangle is x^5/(x+1)  and the width is  (x+1)/x^3.

We'll substitute w and l by the given expressions:

A = (x+1)*x^5/x^3*(x+1)

We'll simplify and we'll get:

A = x^2 (1)

The value of the area is 16 cm^2.

We'll substitute the value of the area in (1):

16 = x^2

x = 4 cm

The length is:

l = x^5/(x+1)

l  = 4^5/5

l = 204.8 cm

The width is:

w = (x+1)/x^3

w = 5/64

w = 0.078 cm

william1941's profile pic

william1941 | College Teacher | (Level 3) Valedictorian

Posted on

We are given that area of a rectangle is 16. The length of the rectangle is x^5/(x+1)  and the width is  (x+1)/x^3.

Now we know that the area is equal to length* width

Here length = x^5/(x+1)

Width = (x+1)/x^3

Therefore [x^5/(x+1)] * [(x+1)/x^3]

Now rearrange the terms so that we can cancel like terms

=> (x^5 / x^3) / (x+1)/(x+1)

=> x^2 / 1

=> x^2

Therefore the area is x^2. We also know x^2 = 16 . Therefore x= sqrt 16 = 4 or -4 , but the dimensions cannot be negative.

Therefore x = 4

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