Ask a New Question
Menu

Use the image to answer the question.

A rectangle is formed from two right triangles. The base of the rectangle measures 80 yards and is labeled Johnson Avenue. The top of the rectangle is labeled Edison Avenue. The left side joining both the avenues is labeled 41st street and measures 60 yards. The right side of the rectangle is labeled 42nd street. A bank is located at the vertex of 41st street and Edison Avenue. The hypotenuse joining the bank and the vertex of Johnson Avenue and 42nd street is labeled park.

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. its not 20

1 answer

To determine how much shorter Sylvia's walk is through the park compared to walking straight down Johnson Avenue and then down 41st Street, we can calculate both distances.

  1. Distance walking straight down Johnson Avenue and 41st Street:

    • The distance along Johnson Avenue: 80 yards
    • The distance along 41st Street: 60 yards
    • Total distance walking straight: \[ 80 + 60 = 140 \text{ yards} \]

  2. Distance walking through the park (the hypotenuse):

    • The right triangle is formed by:
      • Johnson Avenue to 42nd Street (base): 80 yards
      • 41st Street to Edison Avenue (height): 60 yards
    • The distance (hypotenuse, denoted as "park") can be found using the Pythagorean theorem: \[ d = \sqrt{(80^2) + (60^2)} = \sqrt{6400 + 3600} = \sqrt{10000} = 100 \text{ yards} \]

  3. Difference in distances:

    • The difference in walking distances between the two routes: \[ 140 - 100 = 40 \text{ yards} \]

Thus, if Sylvia walks through the park instead of straight down Johnson Avenue and straight down 41st Street, it will be 40 yards shorter.