Question
At summer camp, the swimming course runs the length (L) of a small lake. To determine the length of the course, the camp counselors measure the two "dry" legs of a right triangle. What is the length in meters of the swimming course in the figure below? (1 point)
A right triangle overlaps a lake. It has sides 25 and 40 meters. Hypotenuse labeled L goes through the lake.
a
15 m
b
31 m
c
47 m
d
65 m
A right triangle overlaps a lake. It has sides 25 and 40 meters. Hypotenuse labeled L goes through the lake.
a
15 m
b
31 m
c
47 m
d
65 m
Answers
GPT-4o mini
To find the length of the swimming course (hypotenuse \( L \)) which is the longest side of the right triangle formed by the two legs given:
1. One leg of the right triangle is 25 meters.
2. The other leg of the right triangle is 40 meters.
By using the Pythagorean theorem, which states:
\[
c^2 = a^2 + b^2
\]
where \( c \) is the length of the hypotenuse, and \( a \) and \( b \) are the lengths of the legs, we can solve for \( L \):
\[
L^2 = 25^2 + 40^2
\]
Calculating \( 25^2 \) and \( 40^2 \):
\[
25^2 = 625
\]
\[
40^2 = 1600
\]
Adding these together:
\[
L^2 = 625 + 1600 = 2225
\]
Now, take the square root to find \( L \):
\[
L = \sqrt{2225} \approx 47.17 \text{ meters}
\]
Among the given options, the closest value to \( L \) is:
**c. 47 m**.
1. One leg of the right triangle is 25 meters.
2. The other leg of the right triangle is 40 meters.
By using the Pythagorean theorem, which states:
\[
c^2 = a^2 + b^2
\]
where \( c \) is the length of the hypotenuse, and \( a \) and \( b \) are the lengths of the legs, we can solve for \( L \):
\[
L^2 = 25^2 + 40^2
\]
Calculating \( 25^2 \) and \( 40^2 \):
\[
25^2 = 625
\]
\[
40^2 = 1600
\]
Adding these together:
\[
L^2 = 625 + 1600 = 2225
\]
Now, take the square root to find \( L \):
\[
L = \sqrt{2225} \approx 47.17 \text{ meters}
\]
Among the given options, the closest value to \( L \) is:
**c. 47 m**.