Pythagorean Theorem

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.

The legs of a right triangle are the two sides that form the right angle. They are usually referred to as 'a' and 'b' in the Pythagorean Theorem.

The hypotenuse is the longest side of a right triangle, opposite the right angle. It is denoted as 'c' in the Pythagorean Theorem.

Using the Pythagorean Theorem: 15² + b² = 21²; b² = 21² - 15²; b² = 441 - 225; b² = 216; b = √216 ≈ 14.7 cm.

True.

c = √(a² + b²), where 'c' is the hypotenuse and 'a' and 'b' are the legs.

a = √(c² - b²) or b = √(c² - a²), where 'c' is the hypotenuse and 'a' and 'b' are the legs.

Using the Pythagorean Theorem: 9² + b² = 15²; b² = 15² - 9²; b² = 225 - 81; b² = 144; b = √144 = 12.

Using the Pythagorean Theorem: c = √(8² + 6²); c = √(64 + 36); c = √100; c = 10 cm.

The sum of the squares of the lengths of the legs equals the square of the length of the hypotenuse.