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.
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Answer 1

To find the distance Sylvia would walk if she takes the park route, we need to use the Pythagorean theorem.

The distance from 42nd Street to 41st Street (adjacent side) is 80 yards, and the distance from Johnson Avenue to Edison Avenue (opposite side) is 60 yards.

Let's call the distance through the park (hypotenuse) x yards.

Using the Pythagorean theorem (a^2 + b^2 = c^2), we have:

80^2 + 60^2 = x^2
6400 + 3600 = x^2
10000 = x^2
x = 100 yards

So, the distance Sylvia would walk if she takes the park route is 100 yards.

The distance Sylvia would walk if she goes straight down Johnson Avenue and then right on 41st Street is 80 + 60 = 140 yards.

Therefore, if Sylvia walks through the park instead of straight down the streets, the walk will be 140 - 100 = 40 yards shorter.