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 a right triangle?

Back

A right triangle is a triangle that has one angle measuring 90 degrees.

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 leg of a right triangle is 3 cm and the other leg 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 formula to find the area of a square?

Back

Area = side².

Front

If the hypotenuse of a right triangle is 10 cm and one leg is 6 cm, how do you find the other leg?

Back

Use the Pythagorean Theorem: a² + 6² = 10²; a² + 36 = 100; a² = 64; a = 8 cm.

Front

What is the distance from the top of a ladder to the base of the wall if the ladder is 10 feet long and the base is 4 feet from the wall?

Back

9 feet (using the Pythagorean Theorem: 4² + b² = 10²; 16 + b² = 100; b² = 84; b = √84 ≈ 9.2 feet).

Front

What does √35 represent in the context of right triangles?

Back

√35 can represent the length of a leg in a right triangle when the other leg and the hypotenuse are known.

Front

How do you calculate the height a ladder reaches against a wall?

Back

Use the Pythagorean Theorem: height = √(ladder² - distance from wall²).

Front

If a triangle has a hypotenuse of 12 cm and one leg of 10 cm, what is the length of the other leg?

Back

6.6 cm (using the Pythagorean Theorem: 10² + b² = 12²; 100 + b² = 144; b² = 44; b = √44 ≈ 6.6 cm).