Syivia 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 comer 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?
First, let's calculate the distance Sylvia would have to walk if she goes straight from her house to work.
The distance from 42nd Street to 41st Street is 80 yards.
The distance from Johnson Avenue to Edison Avenue is 60 yards.
So, the total distance Sylvia would have to walk is 80 yards + 60 yards = 140 yards.
Now let's calculate the distance Sylvia would have to walk if she goes through the park.
Since the intersections are at 90-degree angles, we can use the Pythagorean theorem to find the distance she would have to walk.
The distance between 42nd Street and 41st Street is the same as the distance between her house and the bank, which is also 80 yards.
The distance between Johnson Avenue and Edison Avenue is 60 yards.
Using the Pythagorean theorem, we can calculate the distance she would have to walk through the park:
Distance = sqrt((80 yards)^2 + (60 yards)^2)
Distance = sqrt(6400 yards^2 + 3600 yards^2)
Distance = sqrt(10000 yards^2)
Distance = 100 yards
Therefore, it is 140 yards - 100 yards = 40 yards shorter for Sylvia to walk through the park.