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.
To find out how much shorter it is for Sylvia to walk through the park, we can use the Pythagorean theorem.
The distance of walking straight down Johnson Avenue and then turning right on 41st Street forms the hypotenuse of a right triangle, where the two legs are the distances from 42nd Street to 41st Street (80 yards) and from Johnson Avenue to Edison Avenue (60 yards).
Using the Pythagorean theorem, we can find the hypotenuse length:
Hypotenuse^2 = (80 yards)^2 + (60 yards)^2
Hypotenuse^2 = 6400 yards + 3600 yards
Hypotenuse^2 = 10,000 yards
Hypotenuse = √10,000 yards
Hypotenuse = 100 yards
Therefore, walking straight down Johnson Avenue and then turning right on 41st Street is 100 yards.
If Sylvia walks through the park, she will be walking along the two legs of the right triangle, which are 80 yards and 60 yards. Therefore, the distance she would walk through the park is the sum of these two distances:
80 yards + 60 yards = 140 yards
To find out how much shorter it is for Sylvia to walk through the park, we can subtract the distance through the park from the distance of walking straight down Johnson Avenue and then turning right on 41st Street:
100 yards - 140 yards = -40 yards
Therefore, it is 40 yards shorter for Sylvia to walk through the park.