Quiz Of The Pythagorean Theorem

Explanation
Using 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, we can find the value of the hypotenuse. In this case, the lengths of the other two sides are given as a=3 and b=4. Plugging these values into the theorem, we get c^2 = 3^2 + 4^2 = 9 + 16 = 25. Taking the square root of both sides, we find that c = 5. Therefore, the correct answer is 5.

Explanation
In a right triangle, the longest side is called the hypotenuse. The other two sides are called the legs. The hypotenuse is always opposite the right angle, which is 90 degrees. Therefore, the correct answer is hypotenuse. The terms "leg" and "angle" are also mentioned in the question, but they do not refer to the longest side of a right triangle. Degree is a unit of measurement for angles and is not directly related to the sides of a triangle.

Explanation
The Pythagorean Theorem states that in a right 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, we are given the values of b and c, which are the two sides of the right triangle. By substituting the values into the formula a^2 = c^2 - b^2, we can solve for a. Plugging in the given values, we get a^2 = 10^2 - 6^2, which simplifies to a^2 = 100 - 36. Therefore, a^2 = 64, and taking the square root of both sides, we find that a = 8.

Explanation
When finding the hypotenuse, you must take the square root of the value c. The square root is used to find the length of the hypotenuse in a right triangle when the lengths of the other two sides are known. The square of a number is used to find the area of a square or to find the length of a side when the area is known. Double and triple are not applicable in this context.