Suppose a rectangular garden plot has a length that can be expressed as x+2 feet and a width expressed as x+7 feet. Write a polynomial expression to represent the area of the garden? Write a polynomial expression to represent the perimeter of the garden?

Question

contestada

Respuesta :

akposevictor akposevictor · Answer 1 · 2020-10-06T02:22:14+02:00

Answer:

[tex] Area = x^2 + 9x + 14 [/tex]

[tex] Perimeter = 4x + 18 [/tex]

Step-by-step explanation:

Given:

Length of rectangular garden = (x + 2) ft

Width = (x + 7) ft

Required:

a. Polynomial expression of the area of the garden

b. Polynomial expression of the perimeter of the garden

SOLUTION:

Area of the rectangular garden = length × width

[tex] Area = (x + 2)(x + 7) [/tex]

Expand using the distributive property of multiplication

[tex] Area = x(x + 7) +2(x + 7) [/tex]

[tex] Area = x^2 + 7x + 2x + 14 [/tex]

[tex] Area = x^2 + 9x + 14 [/tex]

Perimeter = 2(length) + 2(width)

[tex] Perimeter = 2(x + 2) + 2(x + 7) [/tex]

[tex] Perimeter = 2x + 4 + 2x + 14 [/tex]

Collect like terms

[tex] Perimeter = 2x + 2x + 4 + 14 [/tex]

[tex] Perimeter = 4x + 18 [/tex]