Pythagorean Review

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 for the area of a square?

Back

The area of a square is calculated using the formula: Area = side², where 'side' is the length of one side of the square.

Front

If the area of a square is 25 in², what is the length of one side?

Back

The length of one side of the square is 5 inches, since side = √(Area) = √(25) = 5.

Front

What is the relationship between the sides of a 3-4-5 triangle?

Back

In a 3-4-5 triangle, the lengths of the sides are in a ratio of 3:4:5, which satisfies the Pythagorean theorem, making it a right triangle.

Front

How do you find the hypotenuse of a right triangle if the lengths of the legs are known?

Back

To find the hypotenuse (c) of a right triangle when the lengths of the legs (a and b) are known, use the formula: c = √(a² + b²).

Front

What is the perimeter of a triangle?

Back

The perimeter of a triangle is the sum of the lengths of all three sides. For a triangle with sides a, b, and c, the perimeter P is given by: P = a + b + c.

Front

If a right triangle has legs of lengths 3 cm and 4 cm, what is the length of the hypotenuse?

Back

Using the Pythagorean theorem, the hypotenuse is 5 cm, calculated as: c = √(3² + 4²) = √(9 + 16) = √25 = 5.

Front

What is the area of a triangle?

Back

The area of a triangle can be calculated using the formula: Area = (base × height) / 2.

Front

How do you calculate the area of a triangle with legs of 3 cm and 4 cm?

Back

If the legs are the base and height, the area is: Area = (3 cm × 4 cm) / 2 = 6 cm².

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.