Ted determined that the length of the diagonal of his square-shaped lawn was square foot 83 feet. Which is the closest to the length in feet of the diagonal of Ted's lawn?
A. 8
B. 9
C. 41
D. 166
Is the answer B?
Thank you
No, the answer is not B. The closest length to the diagonal of Ted's lawn is actually C. 41 feet. It's significantly closer to 83 feet than the other options. So, C is the best choice! However, if you ever need a square-shaped lawn with a diagonal of 166 feet, you might need some extra land or a pair of stilts!
To find the length of the diagonal of a square, we can use the Pythagorean theorem.
The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse (diagonal) is equal to the sum of the squares of the lengths of the other two sides.
In this case, the length of one side of the square is 83 feet. Let's call this length "a".
Using the Pythagorean theorem:
a² + a² = diagonal²
2a² = diagonal²
diagonal² = 2a²
diagonal = √(2a²)
Substituting the value of a as 83 feet:
diagonal = √(2 * 83²)
diagonal = √(2 * 6889)
diagonal = √(13778)
diagonal ≈ 117.37 feet
The closest answer choice to the length of the diagonal, 117.37 feet, is C. 41.
To determine the length of the diagonal of a square, we can use the Pythagorean theorem. The Pythagorean theorem states that in a right-angled triangle, the square of the length of the hypotenuse (in this case, the diagonal) is equal to the sum of the squares of the other two sides (in this case, the lengths of the sides of the square lawn).
So, let's consider the square lawn with a diagonal length of 83 feet.
Let's assume that the length of one side of the square lawn is "x" feet. According to the Pythagorean theorem, we have:
x^2 + x^2 = 83^2
Simplifying this equation, we get:
2x^2 = 83^2
Divide both sides by 2:
x^2 = (83^2) / 2
Take the square root of both sides to find x:
x = sqrt[(83^2) / 2]
Now, let's find the closest answer option to this value:
A. 8: Comparing x with 8, we can see that (83^2) / 2 is significantly larger than 8^2. So, A is not the closest answer option.
B. 9: Comparing x with 9, we can see that (83^2) / 2 is still significantly larger than 9^2. So, B is not the closest answer option.
C. 41: Comparing x with 41, we find that (83^2) /2 is slightly smaller than 41^2. So, C could be the closest answer option.
D. 166: Comparing x with 166, we find that (83^2) /2 is significantly smaller than 166^2. So, D is not the closest answer option.
Based on our calculations, the closest answer to the length in feet of the diagonal of Ted's lawn is option C, which is 41 feet.
I agree with your answer of B.
√83 = 9.1104335791442988819456261046887
9.1104335791442988819456261046887 is closer to 9, so I have to agree with your answer.
I hope this helps! :)