The Frostburg-Truth bus travels on a straight road from Frostburg Mall to Sojourner Truth Park. The mall is 2 miles east and 5 miles north of the City Center. The park is 5 miles west and 5 miles south of the Center. How far is it from the mall to the park to the nearest tenth of a mile?
A.13.5 miles
B.12.2 miles
I think its B
To find the distance from the mall to the park, we can break it down into two legs: from the mall to the city center and from the city center to the park.
The distance from the mall to the city center can be found using the Pythagorean theorem, where the two sides are the eastward distance (2 miles) and the northward distance (5 miles).
Using the formula a^2 + b^2 = c^2, we can calculate:
(2 miles)^2 + (5 miles)^2 = c^2
4 + 25 = c^2
c^2 = 29
Taking the square root of both sides, we find that c = √29 miles, approximately 5.4 miles (rounded to the nearest tenth).
Now, let's find the distance from the city center to the park. Using the same process as above, the two sides are the westward distance (5 miles) and the southward distance (5 miles).
Using the formula a^2 + b^2 = c^2, we can calculate:
(5 miles)^2 + (5 miles)^2 = c^2
25 + 25 = c^2
c^2 = 50
Taking the square root of both sides, we find that c = √50 miles, approximately 7.1 miles (rounded to the nearest tenth).
To find the total distance from the mall to the park, we add the distances from the mall to the city center and from the city center to the park:
5.4 miles + 7.1 miles = 12.5 miles (rounded to the nearest tenth).
Therefore, the distance from the mall to the park is approximately 12.5 miles.
So, the correct answer is B. 12.2 miles.
To find the distance from the mall to the park, we can break it down into individual components.
First, let's find the distance from the mall to the City Center. We can use the Pythagorean theorem, which states that in a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.
In this case, the mall is 2 miles east and 5 miles north of the City Center, so we have a right triangle with sides measuring 2 miles and 5 miles.
Using the Pythagorean theorem, we can find the hypotenuse (distance from the mall to the City Center):
Hypotenuse^2 = 2^2 + 5^2
Hypotenuse^2 = 4 + 25
Hypotenuse^2 = 29
Hypotenuse = √29
Next, let's find the distance from the City Center to the park. Similarly, we have a right triangle with sides measuring 5 miles west and 5 miles south of the City Center.
Using the Pythagorean theorem:
Hypotenuse^2 = 5^2 + 5^2
Hypotenuse^2 = 25 + 25
Hypotenuse^2 = 50
Hypotenuse = √50
Finally, to find the total distance from the mall to the park, we add the two distances together:
Total distance = √29 + √50
Now, let's calculate the approximate value to the nearest tenth of a mile:
Total distance ≈ 5.39 + 7.07 ≈ 12.46
Therefore, the distance from the mall to the park is approximately 12.5 miles, which corresponds to option B.