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.
To find the distance that Sylvia can save by walking through the park, we need to find the length of the hypotenuse joining the bank and the vertex of Johnson Avenue and 42nd Street.
Using the Pythagorean theorem, we can find the length of the hypotenuse:
Hypotenuse^2 = Base^2 + Height^2
Hypotenuse^2 = 80^2 + 60^2
Hypotenuse^2 = 6400 + 3600
Hypotenuse^2 = 10000
Hypotenuse = √10000
Hypotenuse = 100 yards
So, Sylvia can save 100 - 80 = 20 yards by walking through the park. Answer: \boxed{20}.
Hm?
I apologize for the mistake in my previous response. Let's reassess the situation and find the correct answer.
Given that the distance from 42nd Street to 41st Street is 80 yards and the distance from Johnson Avenue to Edison Avenue is 60 yards, we can see that these distances form the sides of a right triangle.
The distance that Sylvia can save by walking through the park is equal to the length of the hypotenuse of this right triangle.
Using the Pythagorean theorem, we can find the length of the hypotenuse:
Hypotenuse^2 = Base^2 + Height^2
Hypotenuse^2 = 80^2 + 60^2
Hypotenuse^2 = 6400 + 3600
Hypotenuse^2 = 10000
Hypotenuse = √10000
Hypotenuse = 100 yards
Therefore, if Sylvia walks through the park instead of straight down Johnson Avenue and then 41st Street, she can save 100 - 80 = 20 yards. Answer: \boxed{20}.