Sylvia likes to walk to work when the weather is nice. She works at the bank at the

Question

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 angles, how much shorter is it for Sylvia
to walk through the park?
(1 point)
90°
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 determine how much shorter Sylvia's walk is when she walks through the park instead of down Johnson Avenue and then 41st Street, we can calculate the distance for both routes.

1. Walking down Johnson Avenue and then 41st Street:

   • She walks from her house at 42nd Street and Johnson Avenue to 41st Street, which is 80 yards.
   • Then, she walks from 41st Street down to Edison Avenue, which is 60 yards.
   • Total distance = 80 yards + 60 yards = 140 yards.

2. Walking through the park:

   • Sylvia walks diagonally from 42nd Street and Johnson Avenue to the intersection of 41st Street and Edison Avenue.
   • Since this forms a right triangle (with one leg being 80 yards and the other leg being 60 yards), we can apply the Pythagorean theorem to find the distance:
   • \( c^2 = a^2 + b^2 \)
   • Here, \( a = 80 \) yards and \( b = 60 \) yards:
   • \( c^2 = 80^2 + 60^2 \)
   • \( c^2 = 6400 + 3600 = 10000 \)
   • \( c = \sqrt{10000} = 100 \) yards.

Now we can find out how much shorter Sylvia's walk is through the park compared to the other route:

• Distance when walking directly through the park = 100 yards.
• Distance when walking down Johnson Avenue and 41st Street = 140 yards.

So, the difference is: \[ 140 \text{ yards} - 100 \text{ yards} = 40 \text{ yards}. \]

Thus, Sylvia's walk through the park will be 40 yards shorter than walking down Johnson Avenue and then 41st Street.