Question

The length of a rectangular flower garden is twice the width of the garden. The two shorter sides and one of the longer sides have a two-foot wide walking path bordering the garden.



Part A: Draw the rectangle and side lengths.



Part B: Create a function where, A(x) represents the total area covered by the garden and the walking path given x represents the width of the garden.



Part C. If the width of the garden is 3 feet, what is the total area of the garden and walking path?

Answer 1

Answer:

Area of the figure is 50ft^2.

Step-by-step-explanation:

Let

Breadth of that garden : x ft

Length of that garden : 2x ft { Length of garden = 2 x breadth of garden }

Length of the walking path ( covering breadth ) = ( x + 2 ) ft

Breadth of the walking path ( covering breadth ) = 2 ft

Length of the walking path ( covering length ) = 2x ft

Breadth of the walking path ( covering length ) = 2 ft

Total area = area of path + area of garden

= ( x + 2 )2 + ( x + 2 )2 + ( 2x )2 + ( 2x )x ft^2

= 4x + 8 + 4x + 2x^2 ft^2

= 2x^2 + 8x + 8 ft^2

Function representing the area of garden and path : A(x) = 2x^2 + 8x + 8 .

If x = 3

= > Area of the garden = A(3) = 2( 3 )^2 + 8( 3 ) + 8 = 50 ft^2

This can be solved easily, if the garden & path are treated as a single rectangular figure. In this case,

Length = ( 2x + 4 )ft , breadth = ( x + 2 ) ft

A(x) = ( 2x + 4 )( x + 2 ) = 2x^2 + 4x + 4x + 8 = 2x^2 + 8x + 8.

*A free hand diagram is provided.

Answer 2

Ans. B. The dimensions of the rectangular garden are length = 2x and width = x

The dimensions of the rectangular garden and the walkway are

length = 2x+2 and width = x+4 <--- walkway is on only 1 length but both widths

The area A(x) = (2x+2)(x+4)

= 2x^2 + 8x + 2x + 8

= 2x^2 + 10x + 8

Hope that helps ✌️✌️

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