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 formula to find the length of the hypotenuse in a right triangle?

Back

The formula to find the length of the hypotenuse (c) in a right triangle is c = √(a² + b²), where a and b are the lengths of the other two sides.

Front

How do you determine if a set of three lengths can form a right triangle?

Back

To determine if three lengths can form a right triangle, check if they satisfy the Pythagorean Theorem: a² + b² = c², where c is the longest side.

Front

What are the side lengths of a 3-4-5 triangle?

Back

The side lengths of a 3-4-5 triangle are 3, 4, and 5, which satisfy the Pythagorean Theorem: 3² + 4² = 5².

Front

If one side of a right triangle is 6 cm and the other is 8 cm, what is the length of the hypotenuse?

Back

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

Front

What is the relationship between the sides of a right triangle and the Pythagorean Theorem?

Back

The Pythagorean Theorem establishes a relationship between the lengths of the sides of a right triangle, specifically that the sum of the squares of the two shorter sides equals the square of the longest side.

Front

What is the value of x in the equation 5² + x² = 13²?

Back

To find x, solve the equation: 5² + x² = 13²; 25 + x² = 169; x² = 169 - 25; x² = 144; x = √144 = 12.

Front

What is the significance of the hypotenuse in a right triangle?

Back

The hypotenuse is the longest side of a right triangle, opposite the right angle, and is crucial for applying the Pythagorean Theorem.

Front

Can the lengths 7, 24, and 25 form a right triangle?

Back

Yes, because 7² + 24² = 49 + 576 = 625 = 25², satisfying the Pythagorean Theorem.

Front

What is the area of a right triangle with legs of length 5 cm and 12 cm?

Back

The area of a right triangle is given by the formula: Area = (1/2) * base * height. Here, Area = (1/2) * 5 * 12 = 30 cm².