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
10 yards shorter.
This can be calculated using the Pythagorean theorem.
The distance from 42nd Street to the bank can be found by using the length of Johnson Avenue (80 yards) as one leg and the length of 41st Street (60 yards) as the other leg.
Thus, the distance from 42nd Street to the bank (through Johnson Avenue and 41st Street) is √(80^2 + 60^2) = √(6400 + 3600) = √10000 = 100 yards.
The distance from 42nd Street to the bank through the park is the length of the hypotenuse, which is the same as the length of the shorter path (through the park).
Therefore, the distance through the park is 100 yards, while the distance through Johnson Avenue and 41st Street is 110 yards.
Thus, it is 10 yards shorter for Sylvia to walk through the park.