If the hypotenuse is 41 inches, and one of the legs is 40 inches, what is the length of the other leg in inches?
A. 65
B. 57
C. 25
D. 9
the answer is D.
To find the length of the other leg in a right triangle, we can use the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides.
Let's assign the length of the hypotenuse as 'c' and the lengths of the legs as 'a' and 'b'.
According to the problem:
- Hypotenuse (c) = 41 inches
- Length of one leg (a) = 40 inches
Let's solve for the length of the other leg (b).
Using the Pythagorean theorem:
c^2 = a^2 + b^2
Substituting the given values:
41^2 = 40^2 + b^2
1681 = 1600 + b^2
Rearranging the equation:
b^2 = 1681 - 1600
b^2 = 81
Taking the square root of both sides:
b = √81
b = 9
Therefore, the length of the other leg is 9 inches.
So, the correct answer is option D. 9