Use the Pythagorean Theorem Practice Complete this assessment to review what you've learned. It will not count toward your grade. 4 of 54 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. 4 of 54 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 find the answer, we can use the Pythagorean theorem, which 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 distance from 42nd Street to 41st Street as side A, the distance from Johnson Avenue to Edison Avenue as side B, and the distance through the park as the hypotenuse C.

Using the Pythagorean theorem, we can say:

C^2 = A^2 + B^2

We are given that A = 80 yards and B = 60 yards. Plugging these values into the equation, we get:

C^2 = 80^2 + 60^2
C^2 = 6400 + 3600
C^2 = 10,000

To find C, we take the square root of both sides:

C = √10,000
C = 100 yards

So the distance through the park is 100 yards.

To find how much shorter it is to walk through the park, we subtract the distance via the streets from the distance through the park:

Shorter distance = (60 yards + 80 yards) - 100 yards
Shorter distance = 140 yards - 100 yards
Shorter distance = 40 yards

Therefore, Sylvia can walk 40 yards shorter by taking the park route.