Pythagorean Theorem

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: a² + b² = c².

Front

What type of triangle does the Pythagorean Theorem apply to?

Back

The Pythagorean Theorem only applies to right triangles.

Front

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

Back

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

Front

What is the length of the missing side if one side is 6 m and the hypotenuse is 10 m?

Back

8 m (Using the Pythagorean Theorem: 6² + b² = 10²; 36 + b² = 100; b² = 64; b = 8).

Front

Calculate the diagonal of a rectangle with a width of 8 ft and a length of 15 ft.

Back

17 ft (Using the Pythagorean Theorem: 8² + 15² = 64 + 225 = 289; √289 = 17).

Front

What is the formula to find the length of the hypotenuse in a right triangle?

Back

c = √(a² + b²), where c is the hypotenuse and a and b are the other two sides.

Front

If a right triangle has legs of lengths 5 in. and 12 in., what is the length of the hypotenuse?

Back

13 in. (Using the Pythagorean Theorem: 5² + 12² = 25 + 144 = 169; √169 = 13).

Front

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

Back

In a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.

Front

If the hypotenuse is 13 cm and one leg is 5 cm, what is the length of the other leg?

Back

12 cm (Using the Pythagorean Theorem: 5² + b² = 13²; 25 + b² = 169; b² = 144; b = 12).

Front

What is the Pythagorean triplet?

Back

A Pythagorean triplet consists of three positive integers a, b, and c, such that a² + b² = c². Example: (3, 4, 5).