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 comer 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?
To calculate the distance for Sylvia to walk through the park, we need to calculate the diagonal of a rectangle formed by the streets.
Let's call the distance from 42nd Street to 41st Street (side of the rectangle) = x.
And let's call the distance from Johnson Avenue to Edison Avenue (other side of the rectangle) = y.
Using the Pythagorean theorem, we can find the diagonal (d) of the rectangle:
d² = x² + y²
Since we know x = 80 yards and y = 60 yards:
d² = 80² + 60²
d² = 6400 + 3600
d² = 10000
d = √10000
d = 100 yards
Therefore, the diagonal of the rectangle formed by the streets is 100 yards.
Sylvia's house is at the corner of 42nd Street and Johnson Avenue, while the bank is at the corner of 41st Street and Edison Avenue. Walking through the park would be equivalent to walking along the diagonal of the rectangle.
Since the diagonal is 100 yards and both walking along the streets would involve walking a distance of 80 + 60 = 140 yards,
it is 140 - 100 = 40 yards shorter for Sylvia to walk through the park.