Question

A right triangle has legs of lengths a and b, and a hypotenuse of length c. According to the Pythagorean Theorem, which of the following is true?

a) (a + b) = c
b) a – b = c
c) a + b = c
d) a = b + c

Answer 1

The Pythagorean Theorem states that in a right triangle, the sum of the squares of the lengths of the legs is equal to the square of the length of the hypotenuse. The correct statement according to the Pythagorean Theorem in this case is a + b = c. Example calculation is provided.

Step-by-step explanation:

The Pythagorean Theorem states that in a right triangle, the sum of the squares of the lengths of the legs (a and b) is equal to the square of the length of the hypotenuse (c). This can be expressed as a² + b² = c².

From the given options, the correct statement according to the Pythagorean Theorem is: a + b = c (Option c).

For example, if the lengths of the legs are a = 3 and b = 4, we can calculate the length of the hypotenuse using the Pythagorean Theorem:

1. a² + b² = c²
2. 3² + 4² = c²
3. 9 + 16 = c²
4. 25 = c²
5. c = √25 = 5