A square field has an area of 22,500 square feet. To the nearest foot, what is the diagonal distance across the field?

F. 150 feet
G. 178 feet
H. 191 feet
I. 212 feet
J. 260 feet

c^2 = a^2 + b^2

c^2 = 150^2 + 150^2
c^2 = 22,500 + 22,500
c^2 = 45,000
sqrt(c^2) = sqrt(45,000)
c = 212

I. 212 feet

AREA=SIDE X SIDE

THEREFORE FIND SQUARE ROOT OF 22,500

THEN USE PYTHAGORAS THEOREM Z^2=X^2+Y^2
FIND SQUARE ROOT OF YOUR VALUE.THAT GIVES THE ANSWER TO Z= DIAGONAL

What are the steps to finding the answer to the question: A square field has an area of 22,500 square feet. To the nearest foot, what is the diagonal distance across the field?

Why did the scarecrow go to school?

Because he wanted to be "outstanding" in his field!

To find the diagonal distance across the square field, we can use the Pythagorean theorem. Let's call the side length of the square "s" and the diagonal distance "d". We know that the area of the square is 22,500 square feet, so we can set up the equation:

s^2 = 22,500

Taking the square root of both sides, we find s = √22,500.

Since the diagonal of a square forms a right triangle with two sides of equal length, we can use the Pythagorean theorem to find the diagonal:

d^2 = s^2 + s^2
d^2 = 2s^2
d = √(2s^2)
d = s√2

Plugging in s = √22,500, we get:

d = √22,500 * √2
d = √(22,500 * 2)
d = √45,000
d ≈ 212

So, to the nearest foot, the diagonal distance across the square field is approximately 212 feet.

Therefore, the correct answer is I. 212 feet.

To find the diagonal distance across a square field, we can use the Pythagorean Theorem. The theorem states that in a right-angled triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides.

In this case, the two sides of the square field form a right-angled triangle, with the diagonal as the hypotenuse. Let's call the length of one side of the square "s".

Given that the area of the square field is 22,500 square feet, we can set up the equation:
s^2 = 22,500

To find the length of the diagonal, we need to find the square root of 22,500, and then round it to the nearest foot.

Calculating the square root of 22,500 gives us 150. So the length of one side of the square is 150 feet.

Now, using the Pythagorean Theorem, we can calculate the length of the diagonal (d):
d^2 = s^2 + s^2
d^2 = 150^2 + 150^2
d^2 = 22,500 + 22,500
d^2 = 45,000
d ≈ √45,000 ≈ 212

Rounding 212 to the nearest foot gives us 212 feet. Therefore, the correct answer is (I) 212 feet.

sqrt(22,500) = 150