Question

Scenario: To create the flower gardens, Wendell bought six pieces of wood. Pieces A and B are 6 feet long, pieces C and D are 8 feet long, piece E is 3 feet long, and piece F is 2 feet long.Part 1 of 2 Question: Describe how Wendell can use all six pieces of wood to create either two rectangular gardens or two triangular gardens. Assume the gardens do not share a common side.Part 2 of 2 Question: Wendell’s dog, Jordan, was getting in his way as he worked in the backyard. So, Wendell chained him to a pole. If the chain is 12 feet long, about how much area does Jordan have to walk around?

Answer 1

Given that Wendell bought six pieces of wood. Pieces A and B are 6 feet long, pieces C and D are 8 feet long, piece E is 3 feet long, and piece F is 2 feet long.

1)

We know that rectangles have four sides, to create two rectangles we need two times 4 pieces of wood.

We need 8 pieces of wood to create two rectangles without sharing a common side.

Wendell only has six pieces of wood, so it is not possible to create two rectangles.

We know that triangles have three sides, to create two triangles we need two times 3 pieces of wood.

We need 6 pieces of wood to create two triangles without sharing a common side.

The sum of the two smaller sides of the triangle should be greater than or equal to the third side.

So the triangle with lengths 2,3 and 8 does not make a triangle.

The lengths of the first triangle should be 2,6 and 8.

The lengths of the second triangle should be 3,6 and 8.

Pieces A, C, and F can be used in the first triangle.

Pieces B, D, and E can be used in the second triangle.

The area of the first triangle is

`A_1=\sqrt[]{s(s-a)(s-b)(s-c)}`

where s is the semi perimeter of the triangle.

`s_1=(a+b+c)/(2)`

Substitute a=6, b=8 and c=2, we get

`s_1=(6+8+2)/(2)=(18)/(2)=9\text{ f}eet`

Substitute s=9, a=6, b=8, and c=2 in the area of the triangle, we get

`A_1=\sqrt[]{9(9-6)(9-8)(9-2)}`

`A_1=\sqrt[]{9*3*1*7}=\sqrt[]{189}=13.75\text{ fe}et^2`

The area of the first triangle is 13.75 square feet.

The area of the first triangle is

`A_2=\sqrt[]{s(s-a)(s-b)(s-c)}`

where s is the semi perimeter of the triangle.

`s_2=(a+b+c)/(2)`

Substitute a=6, b=8 and c=3, we get

`s_1=(6+8+3)/(2)=(19)/(2)=9.5\text{ f}eet`

Substitute s=9, a=6, b=8, and c=2 in the area of the triangle, we get

`A_2=\sqrt[]{9.5(9.5-6)(9.5-8)(9,5-2)}`

`A_2=\sqrt[]{9.5*3.5*1.5*7.5}=\sqrt[]{374.0625}=19.34\text{ fe}et^2`

The area of the second triangle is 19.34 square feet.

2)

The length of the chain is 12 feet.

The dog can make a circle with a radius of 12 feet when the dog walks a maximum length from the pole.

The area does Jordan have to walk around = The area of the circle

The area of the circle is

`A=\pi r^2`

Substitute r=12, we get

`A=3.14*12^2`
`A=452.16\text{ f}eet^2`

Hence the area of the dog walk around is 452.16 square feet.