Question

A wild animal generally stays at least x mi from the edge of a forest. For a rectangular forest preserve that is 2 mi
long and 5 mi wide, write a polynomial that represents the area of the available habitat for the wild animal.
(Note: diagram not drawn to scale)

Answer 1

Answer:

$Area = 4x^2 - 14x + 10$

Step-by-step explanation:

See Attachment for Complete Question

Given

$Width = 5mi$ --- For the forest

$Length = 2mi$ -- --- For the forest

Required

Determine the area of the habitat

Since the distance between the animal's habitat is x mi on both sides;

The length and width of the habitat is:

$Width = 5 - (x + x)$

$Width = 5 - 2x$

$Height = 2 - (x +x)$

$Height = 2 - 2x$

The area is then calculated as follows;

$Area = Width * Height$

$Area = (5 - 2x) * (2 - 2x)$

Expand

$Area = 5(2 - 2x) -2x(2 - 2x)$

Open Brackets

$Area = 10 - 10x - 4x + 4x^2$

$Area = 10 - 14x + 4x^2$

Reorder

$Area = 4x^2 - 14x + 10$

Hence; the required polynomial for the habitat area is:

$Area = 4x^2 - 14x + 10$