Question

1. Count the number of squares that make one side of Field A.

Side length = 4 acres (worth 2 points)

2. Count the number of squares that make one side of Field B.

Side length = 3 acres (worth 2 points)

3. Use the Pythagorean Theorem to find the area of Field C in acres:

Area: a² + b² = c2

Hint: You can either square your side lengths when simplifying a² and b², or you can count the squares in each of those fields for the same value.

Area of Field C = blank acres

Answer 1

To solve the problem, we will follow the steps outlined in your questions.

1. For Field A with a side length of 4 acres:
- Since each square is 1 acre, the number of squares that make up one side of Field A is simply 4 acres.
- Thus, for Field A: **4 squares** (worth 2 points).

2. For Field B with a side length of 3 acres:
- Since each square is 1 acre, the number of squares that make up one side of Field B is 3 acres.
- Thus, for Field B: **3 squares** (worth 2 points).

3. To find the area of Field C using the Pythagorean Theorem, we first assume the side lengths represent a right triangle, where:
- a = side of Field A = 4 acres
- b = side of Field B = 3 acres

According to the Pythagorean Theorem:
\[
c^2 = a^2 + b^2
\]
Plugging the values into the equation:
\[
c^2 = 4^2 + 3^2
\]
\[
c^2 = 16 + 9
\]
\[
c^2 = 25
\]

To find c:
\[
c = \sqrt{25} = 5
\]

The area of Field C can be represented as square acres, since it denotes the length of the hypotenuse of the triangle in this context:
- So, the area of Field C = **5 acres**.

Thus, the answers are:
1. 4 squares for Field A
2. 3 squares for Field B
3. Area of Field C = 5 acres