cSylvia likes to walk to work when the weather is nice. She works at the bank at the corner of 41 st 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 down Johnson Avenue and turns right on 41st Street, she will be walking the hypotenuse of a right triangle. The distance from 42nd Street to 41st Street is the vertical leg, which is 80 yards. The distance from Johnson Avenue to Edison Avenue is the horizontal leg, which is 60 yards.
Using the Pythagorean theorem, we can find the length of the hypotenuse:
h^2 = 80^2 + 60^2
h^2 = 6400 + 3600
h^2 = 10000
h = 100 yards
So if Sylvia walks down Johnson Avenue and turns right on 41st Street, the total length of her walk will be 100 yards.
If Sylvia walks through the park, she will be walking along the diagonal of a rectangle. The width of the rectangle is the distance from 42nd Street to 41st Street, which is 80 yards. The length of the rectangle is the distance from Johnson Avenue to Edison Avenue, which is 60 yards.
Using the Pythagorean theorem again, we can find the length of the diagonal:
d^2 = 80^2 + 60^2
d^2 = 6400 + 3600
d^2 = 10000
d = 100 yards
So if Sylvia walks through the park, the total length of her walk will also be 100 yards.
Therefore, it is not shorter for Sylvia to walk through the park. The walk will be 0 yards shorter.
If Sylvia walks through the park instead of straight down Johnson Avenue and straight down 41st Street,
the walk will be how many yards yards shorter.