Use the Pythagorean Theorem Practice Complete this assessment to review what you've learned. It will not count toward your grade. 5 of 55 of 5 Items Question Use the image to answer the question. 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.

Question

Use the Pythagorean Theorem Practice Complete this assessment to review what you've learned. It will not count toward your grade. 5 of 55 of 5 Items Question Use the image to answer the question. 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.

Answer 1

To solve this problem, we can use the Pythagorean Theorem. The Pythagorean Theorem states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.

Let's label the distances as follows:
- Hypotenuse: Distance from 42nd Street to 41st Street (80 yards)
- Other side 1: Distance from 41st Street to Edison Avenue (unknown)
- Other side 2: Distance from Johnson Avenue to Edison Avenue (60 yards)

To find the unknown distance (Other side 1), we can use the Pythagorean Theorem:

80^2 = x^2 + 60^2

Simplifying the equation, we have:

6400 = x^2 + 3600

Subtracting 3600 from both sides:

2800 = x^2

Taking the square root of both sides:

x = √2800 ≈ 52.92 yards

Therefore, if Sylvia walks through the park instead of straight down Johnson Avenue and straight down 41st Street, the walk will be approximately 52.92 yards shorter.