Question

Farmer Bob is planting a garden this spring. He wants to plant squash, pumpkins, corn, beans, and potatoes. His plan for the field layout in feet is shown in the figure below. Use the figure and your knowledge of polynomials, perimeter, and area to solve the following:

For your initial response, answer the two questions below:

1. The farmer needs to spread hay under all the squash plants. Write an expression, using x, that represents the amount of the area of the field just for the squash.

2. The farmer needs a small fence for just around the potato patch. Write an expression, using x, that represents the perimeter of the part of the field just for potatoes. (simplify)

3. Challenge question! Write an expression, using x, that represents the perimeter of the entire garden, should the farmer want a bigger fence. (simplify)

Be sure to explain/show your work on how you determined your answers. Feel free to upload a picture of work or a video explanation to the discussion board.

Answer 1

1.

The farmer needs to spread hay under all the squash plants. Write an expression, using x, that represents the amount of the area of the field just for the squash.

solution

area of rectangle is L x W,

let L =4x and and W = x

therefore Area (A) = 4x(x) = 4x2

2

The farmer needs a small fence for just around the potato patch. Write an expression, using x, that represents the perimeter of the part of the field just for potatoes. (simplify)

solution

parameter(P) = 2( L + W )

let L=x2 - 7x +12 and W = x +6

therefore

P = 2(x2 -7x +12 + x + 6)

= 2( x2 -6x + 18)

P = 2x2 -12x +36

3.

Challenge question! Write an expression, using x, that represents the perimeter of the entire garden, should the farmer want a bigger fence. (simplify)

solution

P= L1+L2+W1+W2

when

L1 = x + 6x +xy -1 = 7x +xy -1

L = 5x + 2 + x2 - 9 +x2 -7x + 12 = 2x2 5x + 2

w1 4x + 5x -2

w2 = xy + x 7

p = 7x +xy -1 + 2x2 5x + 2 + 4x + 5x -2 + xy + x 7

p = 2xy + 2x2 +16x +9

Explanation: