fabianasanchez2008
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A rectangle with a length of x + 5 has a perimeter of 4x + 14.
1. Write the expression for the width of the rectangle in terms of x.
2. Suppose the perimeter of the rectangle is 42 inches. What are the length and
width of the rectangle?
3. Write the expression for the area of the rectangle in terms of x.
4. What is the area of the rectangle when x = 7?
Show how t get the answer

Respuesta :

adioabiola

Answer:

1. Width = x + 2

2. Length = 12; width = 9

3. x² + 7x + 10

4. 108

Step-by-step explanation:

perimeter = 4x + 14

length = x + 5

1. Perimeter of a rectangle = 2(length + width)

4x + 14 = 2{(x + 5) + width}

4x + 14 = 2x + 10 + 2width

4x + 14 - 2x - 10 = 2width

2x + 4 = 2width

Width = (2x + 4)/2

Width = x + 2

2. Perimeter of a rectangle = 2(length + width)

42 = 2{(x + 5) + (x + 2)}

42 = 2x + 10 + 2x + 4

42 = 4x + 14

42 - 14 = 4x

28 = 4x

x = 28/4

x = 7

length = x + 5

= 7 + 5

= 12

Width = x + 2

= 7 + 2

= 9

3. Area of the rectangle = length × width

= (x + 5)(x + 2)

= x² + 2x + 5x + 10

= x² + 7x + 10

4. Area of the rectangle = x² + 7x + 10

When x = 7

x² + 7x + 10

= 7² + 7(7) + 10

= 49 + 49 + 10

= 108

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