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?

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 sh

Answer 1

To calculate the length of the walk through the park, we can use the Pythagorean theorem.

The distance along Johnson Avenue is 80 yards, and the distance along 41st Street is 60 yards. We can treat this as a right-angled triangle, with the diagonal being the distance through the park.

Using the Pythagorean theorem, the length of the diagonal can be calculated as:

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

So, the distance through the park is 100 yards.

To find the difference between the two routes, we subtract the distance through the park from the original distance along Johnson Avenue and 41st Street.

Difference = (80 + 60) - 100
= 140 - 100
= 40 yards

Therefore, it is 40 yards shorter for Sylvia to walk through the park.