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 __ yard shorter
To find out how much shorter it is for Sylvia to walk through the park, we need to calculate the distance of each route.
If Sylvia walks straight down Johnson Avenue and then turns right on 41st Street, the total distance she would walk is the sum of the two legs of the right triangle formed by Johnson Avenue and 41st Street.
The length of Johnson Avenue (one leg of the right triangle) is 80 yards and the length of 41st Street (the other leg of the right triangle) is 60 yards. Using the Pythagorean theorem, we can calculate the hypotenuse (the total distance Sylvia walks):
c^2 = a^2 + b^2
c^2 = 80^2 + 60^2
c^2 = 6400 + 3600
c^2 = 10000
c = 100 yards
So, if Sylvia walks straight down Johnson Avenue and turns right on 41st Street, the total distance she walks is 100 yards.
If Sylvia walks through the park, she is essentially walking along the hypotenuse of the triangle directly from her house to work. Using the Pythagorean theorem, we can calculate the length of this hypotenuse:
c^2 = a^2 + b^2
c^2 = 80^2 + 60^2
c^2 = 6400 + 3600
c^2 = 10000
c = 100 yards
Therefore, the distance she would walk through the park is also 100 yards.
Since both routes are the same length, it is not shorter for Sylvia to walk through the park.