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: c² = a² + b².

Front

What is the formula to find the length of the hypotenuse?

Back

The formula to find the length of the hypotenuse (c) in a right triangle is: c = √(a² + b²).

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

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

Front

What is the area of a square with a side length of 5 in?

Back

The area of a square is calculated as side². Therefore, the area = 5² = 25 in².

Front

If the area of a square is 36 in², what is the length of one side?

Back

The length of one side is found by taking the square root of the area. Therefore, side = √36 = 6 in.

Front

In a right triangle, if one leg is 6 units and the hypotenuse is 10 units, what is the length of the other leg?

Back

Using the Pythagorean Theorem: b = √(c² - a²) = √(10² - 6²) = √(100 - 36) = √64 = 8 units.

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. 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

How do you find the diagonal of a rectangle using the Pythagorean Theorem?

Back

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

Front

If a rectangle has a length of 8 m and a width of 6 m, what is the length of the diagonal?

Back

Using the formula: d = √(8² + 6²) = √(64 + 36) = √100 = 10 m.