Yasin likes to walk to work when the weather is nice. He works at the bank at the corner of 41st Street and Edison Avenue. His house is at the corner of 42nd Street and Johnson Avenue. Assuming that the street intersections are 90° angles, how far does Yasin need to walk if he goes through the park to work? Round your answer to the nearest tenth, if necessary.
To find the distance Yasin needs to walk, we can use the Pythagorean theorem.
We can break down the path into two legs: the distance from Yasin's house to the park, and the distance from the park to his work.
Using the given information, we can see that the distance from Yasin's house to the park is the hypotenuse of a right triangle with legs measuring 1 block in each direction. This creates a right triangle with sides measuring 1 block and 1 block.
By applying the Pythagorean theorem, we can find the length of the hypotenuse:
c^2 = a^2 + b^2
c^2 = 1^2 + 1^2
c^2 = 1 + 1
c^2 = 2
Taking the square root of both sides, we find:
c = √2
So the distance from Yasin's house to the park is approximately √2 blocks.
To find the distance from the park to his work, we can create another right triangle with legs measuring 1 block in each direction. Again, we can apply the Pythagorean theorem to find the length of the hypotenuse.
c^2 = a^2 + b^2
c^2 = 1^2 + 1^2
c^2 = 1 + 1
c^2 = 2
Again, taking the square root of both sides, we find:
c = √2
So the distance from the park to Yasin's work is approximately √2 blocks.
The total distance Yasin needs to walk is the sum of these two distances:
√2 + √2 = 2√2
To find an approximate decimal answer, we can use a calculator to evaluate 2√2:
2√2 ≈ 2.8
Therefore, Yasin needs to walk approximately 2.8 blocks through the park to get to work.
wrong
Apologies for the incorrect response. Let's recalculate the distances correctly.
The distance from Yasin's house to the park can be calculated using the Pythagorean theorem. The two legs of the triangle formed by the streets are 1 block each.
c^2 = a^2 + b^2
c^2 = 1^2 + 1^2
c^2 = 2
c = √2
So, the distance from Yasin's house to the park is √2 blocks.
Similarly, the distance from the park to Yasin's work is also √2 blocks.
To find the total distance Yasin needs to walk, we can add these two distances together:
√2 + √2 = 2√2
Now, let's use a calculator to find a decimal approximation for 2√2:
2√2 ≈ 2.83
Therefore, Yasin needs to walk approximately 2.83 blocks through the park to get to work.
try again
My apologies for the error in my previous responses.
To find the distance Yasin needs to walk if he goes through the park to work, we can break down the path into two legs. The first leg is the distance from Yasin's house to the park, and the second leg is the distance from the park to his work.
From Yasin's house to the park, he needs to walk 42nd Street for one block and then turn onto Johnson Avenue for another block. So the distance of the first leg is 1 block + 1 block = 2 blocks.
From the park to Yasin's work, he needs to walk 41st Street for one block and then turn onto Edison Avenue for another block. Therefore, the distance of the second leg is 1 block + 1 block = 2 blocks.
Now, to find the total distance Yasin needs to walk, we add the distances of the two legs together:
2 blocks + 2 blocks = 4 blocks.
Therefore, Yasin needs to walk a total of 4 blocks to get to work if he goes through the park.
wrong again
Apologies for the repeated errors. Let's recalculate the distances correctly.
The distance from Yasin's house to the park is the sum of the horizontal and vertical distances between the two corners.
The horizontal distance between Yasin's house and the park is 42nd Street - 41st Street = 1 block.
The vertical distance between Yasin's house and the park is Johnson Avenue - Edison Avenue = 42nd Street - 41st Street = 1 block.
To find the diagonal distance (the distance Yasin needs to walk) using the Pythagorean theorem, we can calculate the hypotenuse of the right triangle formed by the horizontal and vertical distances:
c^2 = a^2 + b^2
c^2 = 1^2 + 1^2
c^2 = 2
c ≈ √2
Therefore, the distance Yasin needs to walk from his house to the park is approximately √2 blocks.
The same calculation applies to the distance from the park to Yasin's work, as it is the same distance (1 block horizontally and 1 block vertically).
Hence, the total distance Yasin needs to walk if he goes through the park to work is approximately 2 times √2 blocks, or approximately 2.8 blocks.
Apologies again for the confusion caused by the previous incorrect responses. Thank you for your patience.