Respuesta :
Answer:
Width = 21731 inches .
Step-by-step explanation:
Given : A rectangle has a perimeter of 6x³+9x²-10x+7 and a length of x.
To find : find the width of the rectangle when the length is 19 inches
Solution : We have given
Perimeter = 6x³+9x²-10x+7
x = length
Length = 19.
Width = w .
By the formula of perimeter :
Perimeter = 2 ( length + width)
Plugging the values
6x³+9x²-10x+7 = 2 ( 19 + w).
x = 19 inches.
6(19)³+9(19)²-10(19)+7 = 2( 19 + w).
6(6859) + 9 ( 361) - 190 + 7 = 2 ( 19 + w).
41154 + 3249 -190 + 7 = 2 ( 19 + w).
43500 = 2 ( 19 + w).
On dividing both sides by 2
21750 = 19 + w.
On subtracting both sides by 19
w = 21750 -19.
w = 21731 inches.
Therefore, Width = 21731 inches .
Using the perimeter concept, it is found that:
The width of the rectangle is of 22091 inches.
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Perimeter of a rectangle:
The perimeter of a rectangle of length l and width w is given by:
[tex]P = 2(w + l)[/tex]
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- Length of x means that [tex]l = x[/tex]
- The perimeter is: [tex]P = 6x^3 + 9x^2 - 10x + 7[/tex]
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Since the length is 19: [tex]l = x = 19[/tex]
And
[tex]P = 2(w + l)[/tex]
[tex]6x^3 + 9x^2 - 10x + 7 = 2(w + x)[/tex]
[tex]6(19)^3 + 9(19)^2 - 10(19) + 7 = 2w + 38[/tex]
[tex]44220 - 38 = 2w[/tex]
[tex]2w = 44182[/tex]
[tex]w = \frac{44182}{2}[/tex]
[tex]w = 22091[/tex]
The width of the rectangle is of 22091 inches.
A similar problem is given at https://brainly.com/question/10489198
