Field c is plotted on a grid map in a square with points (4,7)and (7,3) (one square equals 1 acre) use the pythagorean theory to find the area of field c
To find the area of Field C, we need to calculate the distance between the two given points using the Pythagorean theorem, and then square that value to obtain the area.
The Pythagorean theorem states that in a right-angled triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the two other sides.
In this case, the two given points define the sides of a right-angled triangle.
First, let's find the length of the horizontal side (x) of the triangle:
x = 7 - 4 = 3
Next, let's find the length of the vertical side (y) of the triangle:
y = 7 - 3 = 4
Now, we can use the Pythagorean theorem:
hypotenuse^2 = x^2 + y^2
hypotenuse^2 = 3^2 + 4^2
hypotenuse^2 = 9 + 16
hypotenuse^2 = 25
Taking the square root of both sides:
hypotenuse = √25
hypotenuse = 5
Now that we have the length of the hypotenuse, we know that it represents the diagonal of the square field. Since one square on the grid map represents one acre, and the hypotenuse represents the diagonal, we can calculate the area of Field C.
Area = (hypotenuse)^2 = 5^2 = 25 acres
Therefore, the area of Field C is 25 acres.
Can you show the work you used a little simpler math
Apologies for any confusion. Let's simplify the math to find the area of Field C.
Given points (4,7) and (7,3), we can find the side lengths of the triangle formed by these points using simple subtraction.
Horizontal side (x): |7 - 4| = 3 units
Vertical side (y): |7 - 3| = 4 units
Now, we can use the Pythagorean theorem to find the length of the hypotenuse (c), which represents the diagonal of the square field.
c^2 = x^2 + y^2
c^2 = 3^2 + 4^2
c^2 = 9 + 16
c^2 = 25
c = √25
c = 5 units
Since each unit on the grid map represents one acre, the area of Field C is equal to the square of the hypotenuse.
Area = c^2 = 5^2 = 25 acres
Therefore, the area of Field C is 25 acres.
To find the area of field C, we need to calculate the distance between the two given points (4,7) and (7,3) using the Pythagorean theorem, and then square that value.
Step 1: Find the distance between the two points:
The Pythagorean theorem states that in a right 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.
Using the distance formula, we have:
Distance = √((x2 - x1)^2 + (y2 - y1)^2)
Let's substitute the values:
Distance = √((7 - 4)^2 + (3 - 7)^2)
Distance = √(3^2 + (-4)^2)
Distance = √(9 + 16)
Distance = √25
Distance = 5
Step 2: Calculate the area of field C:
Since each square on the grid map represents 1 acre, and the distance we found is in terms of the grid squares, we square the value obtained in Step 1 to get the area of field C.
Area = Distance^2
Area = 5^2
Area = 25 acres
Therefore, the area of field C is 25 acres.