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 total distance Sylvia would have to walk if she goes straight down Johnson Avenue and then down 41st Street is the sum of the distances of each leg of the journey.
Distance = 80 yards + 60 yards = 140 yards
To find the distance if she walks through the park, we can use the Pythagorean theorem since the path through the park forms a right triangle.
Let's call the distance Sylvia has to walk if she goes through the park x yards.
Using the Pythagorean theorem, we get:
x^2 = 80^2 + 60^2
x^2 = 6400 + 3600
x^2 = 10000
x = √10000
x = 100 yards
So, if Sylvia walks through the park, she only has to walk 100 yards.
By subtracting this distance from the total distance of walking down Johnson Avenue and 41st Street, we find the difference:
140 yards - 100 yards = 40 yards
Therefore, it would be 40 yards shorter for Sylvia to walk through the park.