Sophia likes to walk to work when the weather is nice she works at the bank at the corner of 41st St. and Edison Avenue. Her house is at the corner of 42nd St. and Johnson Avenue she can walk down Johnson Avenue and turn right on 41st St. or she can walk through the park the distance from 42nd St. to 41st St. 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 .
To calculate the distance Sophia would have to walk if she takes Johnson Avenue and turns right on 41st St., we need to calculate the length of the two sides of the right triangle formed by Johnson Avenue and 41st St.
Using the Pythagorean theorem, we can calculate the length of the hypotenuse:
c^2 = a^2 + b^2
c^2 = 80^2 + 60^2
c^2 = 6400 + 3600
c^2 = 10000
c = √10000
c = 100 yards
So, if Sophia takes the route through Johnson Avenue and turns right on 41st St., she would have to walk a distance of 100 yards.
Now let's calculate the direct distance through the park from 42nd St. to 41st St.
Again, using the Pythagorean theorem, we can calculate the length of the hypotenuse:
c^2 = a^2 + b^2
c^2 = 80^2 + 60^2
c^2 = 6400 + 3600
c^2 = 10000
c = √10000
c = 100 yards
So, if Sophia takes the route through the park, she would have to walk a distance of 100 yards.
Therefore, it is the same distance for Sophia to walk whether she takes Johnson Avenue or goes through the park.