Question

The diagram below represents the blueprint of a vegetable garden. The beans and potatoes are planted in rectangular gardens. The corn is planted in an area that is represented by a composition of two rectangles. The horizontal lines will represent the lengths of each section of the garden and the vertical lines will represent the widths of each section of the garden. The diagram below represents the blueprint of a vegetable garden. The beans and potatoes are planted in rectangular gardens. The corn is planted in an area that is represented by a composition of two rectangles. The horizontal lines will represent the lengths of each section of the garden and the vertical lines will represent the widths of each section of the garden. Please use the information provided in this diagram to answer questions #1 - 4.

x2 - 7x + 2


x2 + 1







Corn






m



Beans



x - 1




Potatoes

A = x3 - x2 - 30x + 72


x + 6
x2 - 9





Directions: Make sure you show all work for the following questions.
Determine & state the length of the potato garden.

Determine & state the length of m.

Determine & state the perimeter of the corn garden.

Mark said that the area of the bean garden is x3-x2+x-1. Do you agree or disagree with Mark? Explain your answer in complete sentences.

Answer 1

Explanation:

1. The length of the vegetable garden is:

(x² − 7x + 2) + (x² + 1) = 2x² − 7x + 3

The length of the potato garden is therefore:

(2x² − 7x + 3) − (x² − 9) = x² − 7x + 12

2. m + x² + 1 = x² − 7x + 12

m = -7x + 11

3. The perimeter of the corn garden is:

P = (x² − 7x + 2) + (x − 1) + (-7x + 11) + (x + 6) + (x² − 9) + (x + 6) + (x − 1)

P = 2x² − 10x + 14

4. The area of the bean garden is width time length:

A = (x − 1) (x² + 1)

A = x³ − x² + x − 1

Mark is correct.