Use the image to answer the question.
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?
(1 point)
If Sylvia walks through the park instead of straight down Johnson Avenue and straight down 41st Street, the walk will be _ yards shorter.
If Sylvia walks straight down Johnson Avenue and then straight down 41st Street, the total distance she would walk is the sum of the two legs of the right triangle formed by 80 yards and 60 yards. Using the Pythagorean theorem, the hypotenuse (the distance through the park) would be √(80^2 + 60^2) = √(6400 + 3600) = √10000 = 100 yards.
Thus, walking through the park is 40 yards shorter than walking straight down the streets.