ylvia 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?

Question

ylvia 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

To calculate the distance Sylvia would walk if she went through the park, we need to find the hypotenuse of the right triangle formed by Johnson Avenue, the park path, and 41st Street.

Using the Pythagorean theorem:

a^2 + b^2 = c^2

Where:
a = 80 yards
b = 60 yards

(80)^2 + (60)^2 = c^2
6400 + 3600 = c^2
10000 = c^2
c = 100 yards

So, if Sylvia walks through the park, the distance she would walk is 100 yards.

The total distance she would walk if she went straight down Johnson Avenue and then straight down 41st Street is:
80 yards + 60 yards = 140 yards

Therefore, the difference in distance would be:
140 yards - 100 yards = 40 yards

So, it would be 40 yards shorter for Sylvia to walk through the park.