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 shorter.

Answer 1

The distance Sylvia would walk if she goes straight down Johnson Avenue and then right on 41st Street is the hypotenuse of a right triangle with legs of 80 yards and 60 yards. This distance can be calculated using the Pythagorean theorem:

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, if Sylvia walks straight down Johnson Avenue and then right on 41st Street, she would walk 100 yards.

The distance Sylvia would walk if she goes through the park is the sum of the two legs of the right triangle, which is 80 yards + 60 yards = 140 yards.

Therefore, if Sylvia walks through the park instead of straight down Johnson Avenue and then right on 41st Street, the walk would be 100 yards - 140 yards = 40 yards shorter.