Pythagorean Theorem & Geometric Mean

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 is the hypotenuse in a right triangle?

Back

The hypotenuse is the longest side of a right triangle, opposite the right angle.

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 geometric mean of two numbers a and b?

Back

The geometric mean of two numbers a and b is the square root of their product, expressed as √(a*b).

Front

In a right triangle, if the lengths of the two legs are 6 cm and 8 cm, what is the length of the hypotenuse?

Back

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

Front

What is the formula to find the diagonal of a rectangle?

Back

The diagonal (d) of a rectangle can be found using the formula: d = √(length² + width²).

Front

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

Back

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

Front

What is the relationship between the sides of a 30-60-90 triangle?

Back

In a 30-60-90 triangle, the lengths of the sides are in the ratio 1:√3:2, where the shortest side is opposite the 30° angle.

Front

What is the relationship between the sides of a 45-45-90 triangle?

Back

In a 45-45-90 triangle, the lengths of the legs are equal, and the hypotenuse is √2 times the length of each leg.

Front

If the diagonal of a square is 10 cm, what is the length of each side?

Back

Each side is approximately 7.07 cm (Using the formula: side = diagonal/√2).