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 is the longest side of a right triangle called?

Back

The longest side of a right triangle is called the hypotenuse.

Front

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

Back

Using the Pythagorean theorem: c² = 3² + 4² = 9 + 16 = 25, so c = 5 feet.

Front

How do you calculate the diagonal of a rectangle using the Pythagorean theorem?

Back

The diagonal (d) can be calculated using the formula d = √(a² + b²), where a and b are the lengths of the sides of the rectangle.

Front

What is the value of 'x' in the equation 21² – 15² = x²?

Back

x = √(21² - 15²) = √(441 - 225) = √216 = 14.7.

Front

In a right triangle, if one leg measures 9 units and the other leg measures 40 units, what is the length of the hypotenuse?

Back

Using the Pythagorean theorem: c² = 9² + 40² = 81 + 1600 = 1681, so c = 41 units.

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 legs equals the square of the hypotenuse.

Front

If a triangle has sides of lengths 5, 12, and 13, is it a right triangle?

Back

Yes, because 5² + 12² = 25 + 144 = 169 = 13².

Front

What is the formula for finding the area of a right triangle?

Back

The area (A) of a right triangle can be calculated using the formula A = (1/2) * base * height.

Front

How can the Pythagorean theorem be applied in real life?

Back

The Pythagorean theorem can be used in various real-life situations, such as determining the height of a ladder needed to reach a certain height when placed at a distance from the wall.