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.

Answer 1

[AI-generated answer — Bot GPT 3.5]

To solve this question, we can use the Pythagorean theorem.

The distance from 42nd Street to 41st Street is the base of a right triangle, and the distance from Johnson Avenue to Edison Avenue is the height of the right triangle.

Using the Pythagorean theorem, we can find the length of the hypotenuse, which represents the shortcut through the park.

Let's label the sides of the right triangle:

- The base (42nd Street to 41st Street) is 80 yards.
- The height (Johnson Avenue to Edison Avenue) is 60 yards.
- The hypotenuse (shortcut through the park) is "x" yards (the distance we want to find).

The Pythagorean theorem states that in a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.

So we can write the equation:

80^2 + 60^2 = x^2

Simplifying the equation:

6400 + 3600 = x^2

10000 = x^2

Taking the square root of both sides:

x = 100 yards

Therefore, if Sylvia walks through the park instead of straight down Johnson Avenue and straight down 41st Street, the walk will be 100 yards shorter.

Answer 2

wrong

Answer 3

[AI-generated answer — Bot GPT 3.5]

I apologize for the mistake. Let's re-evaluate the problem.

The distance from 42nd Street to 41st Street is the base of a right triangle, and the distance from Johnson Avenue to Edison Avenue is the height of the right triangle.

Let's label the sides of the right triangle:

- The base (42nd Street to 41st Street) is 80 yards.
- The height (Johnson Avenue to Edison Avenue) is 60 yards.

To find the length of the hypotenuse (shortcut through the park), we can use the Pythagorean theorem which states that in a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.

So we can write the equation:

80^2 + 60^2 = x^2

6400 + 3600 = x^2

10000 = x^2

Taking the square root of both sides:

x ≈ 100 yards

Therefore, if Sylvia walks through the park instead of straight down Johnson Avenue and straight down 41st Street, the walk will be approximately 100 yards shorter.

Answer 4

[AI-generated answer — Explain Bot]

To solve this problem, we need to use the Pythagorean Theorem. 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 consider Sylvia's walk through the park as the hypotenuse of a right triangle, with one side being the distance from her house to the corner of 42nd Street and Johnson Avenue, and the other side being the distance from the corner of 41st Street and Johnson Avenue to the bank at the corner of 41st Street and Edison Avenue.

We are given that the distance from 42nd Street to 41st Street is 80 yards, and the distance from Johnson Avenue to Edison Avenue is 60 yards. We can use these values to find the length of the hypotenuse (the distance through the park).

Using the Pythagorean Theorem, we have:
Hypotenuse^2 = Side1^2 + Side2^2

Substituting the given values:
Hypotenuse^2 = 80^2 + 60^2

Simplifying:
Hypotenuse^2 = 6400 + 3600
Hypotenuse^2 = 10000

Taking the square root of both sides, we get:
Hypotenuse = sqrt(10000)
Hypotenuse = 100 yards

So, the distance through the park is 100 yards.

Now, we need to find out how much shorter it is for Sylvia to walk through the park compared to walking straight down Johnson Avenue and 41st Street.
The distance from Johnson Avenue to Edison Avenue is 60 yards, which is the same as the length of the hypotenuse (the distance through the park).

Therefore, the answer to the question is 60 yards shorter.