Samantha leaves her house and drives 18 kilometers east to her friend's house. She then drives north to school. Finally, she drives 30 kilometers directly home, in a straight line, from school. A map of Samantha's route is provided below.
How far does Samantha drive traveling from her friend's house to the school?
A.
35 kilometers
B.
12 kilometers
C.
42 kilometers
D.
24 kilometers
The distance Samantha drives from her friend's house to the school can be found by calculating the hypotenuse of a right triangle with legs of 18 kilometers and 30 kilometers. Using the Pythagorean theorem, we have:
distance^2 = 18^2 + 30^2
distance^2 = 324 + 900
distance^2 = 1224
Taking the square root of both sides, we find:
distance = √1224
Calculating the square root of 1224, we find that the distance Samantha drives from her friend's house to the school is approximately 35.07 kilometers.
Therefore, the correct answer is A. 35 kilometers.
From the information provided, we can see that Samantha drives 18 kilometers east to her friend's house and then drives north to reach school. The map does not specify the distances for these two legs of her journey.
To find the distance Samantha drives from her friend's house to school, we can use the Pythagorean theorem.
The Pythagorean theorem states that in a right-angled 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 lengths of the other two sides.
In this case, the distance Samantha drives east is the base of the right-angled triangle, the distance she drives north is the height, and the direct distance from her friend's house to school is the hypotenuse.
Let's call the distance Samantha drives east "b" and the distance she drives north "h".
Using the Pythagorean theorem, we have:
b^2 + h^2 = hypotenuse^2
Since we do not know the values of b and h, we cannot directly determine the value of the hypotenuse.
Therefore, we cannot accurately determine the distance Samantha drives from her friend's house to school based on the information given.
To determine how far Samantha drives from her friend's house to the school, we need to calculate the distance of the total path she takes.
First, we know that Samantha drives 18 kilometers east from her house to her friend's house.
Then, she drives from her friend's house to the school, but we aren't given the specific distance or direction. However, based on the information provided, we can see that Samantha drives in a straight line for 30 kilometers directly home from school. This means that the distance traveled from her friend's house to the school will be the remaining distance that adds up to 30 kilometers when combined with the 18 kilometers driven east initially.
To calculate this remaining distance, we can use the Pythagorean theorem, which states that the square of the hypotenuse of a right triangle is equal to the sum of the squares of the other two sides.
In this case, the distance from her friend's house to the school can be represented as the hypotenuse of a right triangle, with 18 kilometers being one side and the remaining distance as the other side.
Using the Pythagorean theorem, we can solve for the remaining distance:
Remaining distance = √(30^2 - 18^2)
Calculating this, we get:
Remaining distance = √(900 - 324) = √576 = 24 kilometers
Therefore, the correct answer is D. Samantha drives 24 kilometers from her friend's house to the school.