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Sylvia 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?
If Sylvia walks through the park instead of straight down Johnson Avenue and straight down 41st Street, the walk will be
Apologies for the mistake. Let's recalculate the correct answer.
If Sylvia walks through the park, she will be taking the diagonal line as the hypotenuse of a right triangle. The horizontal side of the triangle is the distance from 42nd Street to 41st Street (80 yards), and the vertical side is the distance from Johnson Avenue to Edison Avenue (60 yards).
Using the Pythagorean theorem:
h^2 = a^2 + b^2
where h is the length of the diagonal line through the park, and a and b are the lengths of the horizontal and vertical sides, respectively.
In this case, a = 80 yards and b = 60 yards. Let's calculate h:
h^2 = 80^2 + 60^2
h^2 = 6400 + 3600
h^2 = 10000
Again, taking the square root of both sides:
h = √10000
h = 100 yards
So, the diagonal line through the park is 100 yards long.
To find how much shorter it is for Sylvia to walk through the park, we subtract the distance she would walk straight down Johnson Avenue and straight down 41st Street (80 + 60 = 140 yards) from the length of the diagonal line through the park (100 yards):
140 - 100 = 40 yards
Therefore, it is 40 yards shorter for Sylvia to walk through the park instead of straight down Johnson Avenue and 41st Street.
To calculate the distance Sylvia would have to walk through the park, we can use the Pythagorean theorem.
The distance from 42nd Street to 41st Street is the horizontal side of a right triangle, and the distance from Johnson Avenue to Edison Avenue is the vertical side. The diagonal line through the park is the hypotenuse.
Using the Pythagorean theorem:
h^2 = a^2 + b^2
where h is the length of the diagonal line through the park, and a and b are the lengths of the horizontal and vertical sides, respectively.
In this case, a = 80 yards and b = 60 yards. Let's calculate h:
h^2 = 80^2 + 60^2
h^2 = 6400 + 3600
h^2 = 10000
Taking the square root of both sides, we get:
h = √10000
h = 100 yards
Therefore, it is 100 yards shorter for Sylvia to walk through the park instead of straight down Johnson Avenue and 41st Street.
I did that and that answer does not work
Thank you that worked
You're welcome! I'm glad the answer worked this time. If you have any more questions, feel free to ask.
To determine how much shorter it is for Sylvia to walk through the park, we can calculate the distances for both routes and compare them.
First, let's calculate the distance for Sylvia to walk straight down Johnson Avenue and then right on 41st Street:
The distance from 42nd Street to 41st Street is given as 80 yards.
The distance from Johnson Avenue to Edison Avenue is given as 60 yards.
To calculate the total distance for this route, we need to add the distances for each leg of the walk:
Distance = 80 yards + 60 yards = 140 yards
Now, let's calculate the distance for Sylvia to walk through the park:
Since the intersections are 90° angles and Sylvia's house is at the corner of 42nd Street and Johnson Avenue, we can form a right-angled triangle. The length of the two legs of the right triangle corresponds to the distances Sylvia would walk along Johnson Avenue and 41st Street.
Using the Pythagorean theorem, we can calculate the hypotenuse of the right triangle, which represents the distance of walking through the park:
Hypotenuse = √(leg₁² + leg₂²)
= √(80² + 60²)
≈ √(6400 + 3600)
≈ √10000
≈ 100 yards
So, the distance for Sylvia to walk through the park is approximately 100 yards.
To find out how much shorter it is for Sylvia to walk through the park, we need to subtract the distance of walking through the park from the distance of the straight route:
Shorter Distance = Distance (Straight Route) - Distance (Through Park)
= 140 yards - 100 yards
= 40 yards
Therefore, it is 40 yards shorter for Sylvia to walk through the park compared to straight down Johnson Avenue and then right on 41st Street.