Pythagorean Theorem

Answer 1

The Pythagorean Theorem states that in a right-angled triangle, the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides. Mathematically, it can be represented as:

c^2 = a^2 + b^2

where c is the length of the hypotenuse, and a and b are the lengths of the other two sides.

This theorem is named after the ancient Greek mathematician Pythagoras, who is credited with its discovery. It is widely used in geometry and has many practical applications in fields like engineering, architecture, and physics.

Answer 2

Ok so solve this and 1 acre = 4,840 sq yards also there are two other squares one is 16 acres and the other is 9 acres
Use the Pythagorean Theorem to find the area of Field C in acres:
Area = a2 + b2 = c2
Area = acres

Answer 3

To find the area of Field C in acres using the Pythagorean Theorem, we need to find the lengths of the sides of the right-angled triangle formed by the three squares.

Let's assume that Field C is the hypotenuse (c) of the triangle. The two other sides are the square with an area of 16 acres (a) and the square with an area of 9 acres (b).

Using the formula a = sqrt(Area), we can find the lengths of sides a and b:
a = sqrt(16) = 4
b = sqrt(9) = 3

Now, we can apply the Pythagorean Theorem:
c^2 = a^2 + b^2
c^2 = 4^2 + 3^2
c^2 = 16 + 9
c^2 = 25

Taking the square root of both sides, we get:
c = sqrt(25) = 5

Now, we know the length of the hypotenuse (c) is 5. To find the area of Field C, we need to convert it from square yards to acres.

Given 1 acre = 4,840 square yards:
Area in acres = Area in square yards / 4,840
Area in acres = (5^2) * 4,840

Area in acres = 25 * 4,840
Area in acres = 121,000

Hence, the area of Field C is 121,000 acres.

Answer 4

ummm i know that's wrong because the number is way to big

Answer 5

Apologies for the incorrect calculation. Let's re-calculate the area of Field C using the correct method:

Given:
Area of Field A = 16 acres
Area of Field B = 9 acres
1 acre = 4,840 square yards

First, we need to find the lengths of the sides of the right-angled triangle formed by Field A and Field B.

Using the formula a = sqrt(Area), we find:
Side a = sqrt(16) = 4 acres
Side b = sqrt(9) = 3 acres

Now, applying the Pythagorean Theorem:
c^2 = a^2 + b^2
c^2 = 4^2 + 3^2
c^2 = 16 + 9
c^2 = 25

Taking the square root of both sides:
c = sqrt(25) = 5 acres

Now, we know the length of the hypotenuse (c) is 5 acres. To find the area of Field C, we need to convert it from square yards to acres.

Using 1 acre = 4,840 square yards:
Area in acres = Area in square yards / 4,840
Area in acres = (5^2) * 4,840

Area in acres = 25 * 4,840
Area in acres = 121,000 square yards / 4,840
Area in acres = 25 acres

Hence, the area of Field C is 25 acres.