Question

Use the Pythagorean Theorem Practice%0D%0AComplete this assessment to review what you've learned. It will not count toward your grade.%0D%0A5 of 55 of 5 Items%0D%0A%0D%0AQuestion%0D%0AUse the image to answer the question.%0D%0A%0D%0A%0D%0A%0D%0ASylvia likes to walk to work when the weather is nice. She works at the bank at the corner of 41st Street and Edison Avenue. Her house is at the corner of 42nd Street and Johnson Avenue. She can walk down Johnson Avenue and turn right on 41st Street, or she can walk through the park. The distance from 42nd Street to 41st Street is 80 yards, and it is 60 yards from Johnson Avenue to Edison Avenue. Assuming the street intersections are 90° angles, how much shorter is it for Sylvia to walk through the park?%0D%0A%0D%0A(1 point)%0D%0AIf Sylvia walks through the park instead of straight down Johnson Avenue and straight down 41st Street, the walk will be yards shorter. its nort 100

Answer 1

[AI-generated answer — Bot GPT 3.5]

To determine how much shorter the walk through the park is, we need to calculate the distance of both routes using the Pythagorean Theorem.

The distance of walking straight down Johnson Avenue and then straight down 41st Street can be calculated using the Pythagorean Theorem:

d = √(80^2 + 60^2)
d = √(6400 + 3600)
d = √10000
d = 100 yards

Now, let's calculate the distance of walking through the park. Since the street intersections are at 90° angles, we can use the Pythagorean Theorem again to determine the distance:

d = √(80^2 + 60^2)
d = √(6400 + 3600)
d = √10000
d = 100 yards

The distance of walking through the park is also 100 yards.

Therefore, if Sylvia walks through the park instead of straight down Johnson Avenue and straight down 41st Street, the walk will be 0 yards shorter.

Answer 2

wroonnnggg

Answer 3

[AI-generated answer — Bot GPT 3.5]

Apologies for the mistake. Let's calculate it correctly:

To determine the distance of walking straight down Johnson Avenue and then straight down 41st Street, we can use the Pythagorean Theorem:

d1 = √(80^2 + 60^2)
d1 = √(6400 + 3600)
d1 = √10000
d1 = 100 yards

Now, let's calculate the distance of walking through the park. Since the street intersections are at 90° angles, we can use the Pythagorean Theorem:

d2 = √(80^2 + 60^2)
d2 = √(6400 + 3600)
d2 = √10000
d2 = 100 yards

Both distances are the same, 100 yards.

Therefore, if Sylvia walks through the park instead of straight down Johnson Avenue and straight down 41st Street, the walk will be the same length. The difference is 0 yards shorter.

Answer 4

wrong

Answer 5

[AI-generated answer — Bot GPT 3.5]

Apologies for the incorrect response earlier. Let's solve the problem correctly this time.

To determine the distance of walking straight down Johnson Avenue and then straight down 41st Street, we can use the Pythagorean Theorem:

d1 = √(80^2 + 60^2)
d1 = √(6400 + 3600)
d1 = √10000
d1 = 100 yards

Now, let's calculate the distance of walking through the park. The park forms a right triangle with sides of 80 yards and 60 yards. If Sylvia walks through the park, she will be walking along the hypotenuse of this triangle.

d2 = √(80^2 + 60^2)
d2 = √(6400 + 3600)
d2 = √10000
d2 = 100 yards

Both distances are the same, 100 yards.

Therefore, if Sylvia walks through the park instead of straight down Johnson Avenue and straight down 41st Street, the walk will be the same length. The difference is 0 yards shorter.

Answer 6

[AI-generated answer — Explain Bot]

To solve this problem using the Pythagorean Theorem, we need to find the length of the hypotenuse of a right triangle.

First, let's draw a diagram to illustrate the given information:

```
C
/|
/ |
80/ |
/ | 60
/ |
/ |
A------B
```

Here, A represents Sylvia's house at the corner of 42nd Street and Johnson Avenue, B represents the bank at the corner of 41st Street and Edison Avenue, and C represents the point where Sylvia could walk through the park.

We are given that the distance from A to B is 80 yards (AB = 80) and the distance from A to C is 60 yards (AC = 60).

To find the length of BC (the shortcut through the park), we can apply the Pythagorean Theorem which states that in a right triangle, the square of the length of the hypotenuse (BC) is equal to the sum of the squares of the other two sides (AB and AC):

BC^2 = AB^2 + AC^2

Substituting the given values:

BC^2 = 80^2 + 60^2

BC^2 = 6400 + 3600

BC^2 = 10000

Taking the square root of both sides of the equation:

BC ≈ √10000

BC ≈ 100

Therefore, the length of BC (the shortcut through the park) is approximately 100 yards.

To calculate how much shorter it is for Sylvia to walk through the park, we need to find the difference between the length of BC and the length of AB:

Shorter distance = AB - BC = 80 - 100 = -20 yards

So, it is actually 20 yards longer for Sylvia to walk through the park compared to straight down Johnson Avenue and straight down 41st Street.

Please note that since the length of BC is greater than AB, we get a negative value indicating the difference in the opposite direction.