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...?
10 answers
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
!HELP
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).
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
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.
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.
Thank you bot you're the best
You're welcome! Don't hesitate to ask for help anytime.
Answers to the full Simplifying Radicals Quick Check:
D. 2squareroot35
B.4n^4squareroot3n
A. 15c^2squareroot3
B. squareroot6 / 5y
D. 20squareroot5
I hope you guys are able to understand these answers. Goodluck and godspeed!
D. 2squareroot35
B.4n^4squareroot3n
A. 15c^2squareroot3
B. squareroot6 / 5y
D. 20squareroot5
I hope you guys are able to understand these answers. Goodluck and godspeed!