A gardener is mowing a 20 by 40 yard rectangular pasture using a diagonal pattern. He mows from one corner of the pasture to the corner diagonally opposite. What is the length of this pass with the mower? Give your answer in simplified form.
A.10 sq rt 20
B.20 sq rt 2
C.400 sq rt 5
D.20 sq rt 5
I think it is D...?
correct,
Thank you
Would you please show me how you arrived at that answer. I do not know how to set up the problem to get the answer. Thanks
I apologize for the mistake, you are correct. The answer choice should be D, 20sqrt(5), not B, 20sqrt(2).
Using the Pythagorean Theorem as shown above, we have:
diagonal^2 = 20^2 + 40^2
diagonal^2 = 400 + 1600
diagonal^2 = 2000
Taking the square root of both sides, we get:
diagonal = sqrt(2000)
Simplifying as before, we get:
diagonal = 20sqrt(5)
Therefore, the length of the pass with the mower is 20sqrt(5) yards.
You're welcome! Don't hesitate to ask for help anytime.
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Sure, I can help with that!
We can use the Pythagorean Theorem to find the length of the diagonal which will give us the length of the pass with the mower.
The Pythagorean Theorem states that in a right triangle, the sum of the squares of the two legs (sides adjacent to the right angle) is equal to the square of the hypotenuse (the side opposite the right angle).
In this case, the rectangular pasture is a right triangle with legs of length 20 and 40 yards. The diagonal of the pasture is the hypotenuse of this right triangle.
So, using the Pythagorean Theorem, we have:
diagonal^2 = 20^2 + 40^2
diagonal^2 = 400 + 1600
diagonal^2 = 2000
Taking the square root of both sides, we get:
diagonal = sqrt(2000)
We can simplify this by factoring out the largest perfect square that divides into 2000, which is 4:
diagonal = sqrt(4 * 500)
diagonal = 2sqrt(500)
We can simplify this further by factoring the 500 into the product of its prime factors:
diagonal = 2sqrt(2 * 2 * 5 * 5 * 5)
diagonal = 2 * 5sqrt(2 * 5 * 5)
diagonal = 10sqrt(50)
diagonal = 10sqrt(25 * 2)
diagonal = 10 * 5sqrt(2)
diagonal = 50sqrt(2)
Therefore, the length of the pass with the mower is 50sqrt(2) yards, which is answer choice B, 20sqrt(2).
The bot is wrong, the answer choice is D
Thank you bot you're the best
To find the length of the diagonal pass with the mower, we can use the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the other two sides.
In this case, the length of one side of the rectangle is 20 yards, and the length of the other side is 40 yards. Let's label the sides as follows:
a = 20 yards (length of one side)
b = 40 yards (length of the other side)
c = ? (diagonal length)
We want to find the length of the diagonal, which is c. Applying the Pythagorean theorem, we have:
c^2 = a^2 + b^2
c^2 = 20^2 + 40^2
c^2 = 400 + 1600
c^2 = 2000
To simplify the answer, we can look for perfect square factors of 2000.
The square root of 2000 is approximately 44.72. However, because the answer choices are in simplified form, we need to simplify it further.
Taking out the perfect square factor, we can write 2000 as 400 * 5.
Thus, c = √(2000) = √(400 * 5)
Simplifying further, we have c = 20 * √5
Therefore, the correct answer is D) 20√5, as you correctly guessed.