Pythagorean Theorem - Finding the hypotenuse

Front

What is the Pythagorean Theorem?

Back

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

Front

How do you find the hypotenuse of a right triangle?

Back

To find the hypotenuse (c) of a right triangle, use the formula: c = √(a² + b²), where a and b are the lengths of the other two sides.

Front

If one side of a right triangle is 3 and the other side is 4, what is the length of the hypotenuse?

Back

Using the Pythagorean Theorem: c = √(3² + 4²) = √(9 + 16) = √25 = 5.

Front

What is the length of the hypotenuse if the two other sides are 6 and 8?

Back

c = √(6² + 8²) = √(36 + 64) = √100 = 10.

Front

In a right triangle, if the hypotenuse is 13 and one side is 5, what is the length of the other side?

Back

Using the Pythagorean Theorem: b = √(c² - a²) = √(13² - 5²) = √(169 - 25) = √144 = 12.

Front

What is the relationship between the sides of a right triangle?

Back

In a right triangle, the sum of the squares of the two shorter sides equals the square of the longest side (the hypotenuse).

Front

If a right triangle has sides of length 9 and 12, what is the length of the hypotenuse?

Back

c = √(9² + 12²) = √(81 + 144) = √225 = 15.

Front

What is the distance formula derived from the Pythagorean Theorem?

Back

The distance between two points (x1, y1) and (x2, y2) in a coordinate plane is given by: d = √((x2 - x1)² + (y2 - y1)²).

Front

If a right triangle has a hypotenuse of 10 and one side of 6, what is the length of the other side?

Back

b = √(10² - 6²) = √(100 - 36) = √64 = 8.

Front

What is the Pythagorean triple?

Back

A Pythagorean triple consists of three positive integers a, b, and c, such that a² + b² = c². An example is (3, 4, 5).