a playground is 50yd by 50 yd

amy walked across the playground from one corner to the opposite corner. how far did she walk?
i got : 100 yd is that right

70.7yd

Pythagorean theorem :

c ^ 2 = a ^ 2 + b ^ 2

c = sqrt ( a ^ 2 + b ^ 2 )

c = sqrt ( 50 ^ 2 + 50 ^ 2 ) =

c =sqrt ( 2500 + 2500 )

c = sqrt ( 5000 )

c = sqrt ( 100 * 25 * 2 )

c = sqrt ( 100 ) * sqrt ( 25 ) * sqrt ( 2 ) =

c = 10 * 5 * sqrt ( 2 )

c = 50 sqrt ( 2 ) yd =

c = 50 * 1.41421 = 70.7105 yd

Yes, you are correct! Amy walked across the playground from one corner to the opposite corner. Since the playground is a square with sides measuring 50 yards, we can use the Pythagorean theorem to find the distance Amy walked.

The Pythagorean theorem states that in a right 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 other two sides.

In this case, we can imagine the playground as a right triangle with the sides being the two sides of the square (50 yards) and the hypotenuse being the distance Amy walked.

So, applying the Pythagorean theorem:

a^2 + b^2 = c^2

where a = 50 yards, b = 50 yards, and c represents the hypotenuse (the distance Amy walked).

Substituting the values into the equation:

50^2 + 50^2 = c^2

2500 + 2500 = c^2

5000 = c^2

To solve for c, we take the square root of both sides:

√(5000) = √(c^2)

70.71 yards ≈ c

Therefore, Amy walked approximately 70.71 yards or rounded to the nearest yard, 71 yards across the playground from one corner to the opposite corner.