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.

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.

Answer 1

Sylvia can walk through the park by taking a diagonal route from 42nd Street to 41st Street. This forms a right triangle with legs of 80 yards and 60 yards.

Using the Pythagorean theorem, we can find the length of the diagonal:

c^2 = a^2 + b^2
c^2 = 80^2 + 60^2
c^2 = 6400 + 3600
c^2 = 10000
c = √10000
c = 100 yards

So, the diagonal route through the park is 100 yards.

The total distance Sylvia saves by walking through the park instead of straight down Johnson Avenue and 41st Street is:

(80 yards + 60 yards) - 100 yards = 40 yards

Therefore, Sylvia saves 40 yards by walking through the park.