60 yd.
41st St.
bank
Edison Ave.
park
Johnson Ave.
80 yd.
42nd St.
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.
The distance Sylvia would walk if she goes straight down Johnson Avenue and 41st Street is:
60 yd (Johnson Ave) + 80 yd (42nd St to 41st St) + 60 yd (Edison Ave) = 200 yd
If Sylvia walks through the park, she would walk the hypotenuse of a right triangle with legs of 60 yd and 80 yd:
√(60^2 + 80^2) = √(3600 + 6400) = √10000 = 100 yd
So, the walk through the park is 100 yards, and the difference in distance is:
200 - 100 = 100 yards
Therefore, it is 100 yards shorter for Sylvia to walk through the park.