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 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 one side of a square is 5 cm, what is its area?

Back

Area = 5 cm × 5 cm = 25 cm².

Front

What is the relationship between the sides of a right triangle?

Back

In a right triangle, the lengths of the sides are related by the Pythagorean Theorem: a² + b² = c², where c is the hypotenuse.

Front

How do you find the length of the hypotenuse in a right triangle?

Back

To find the length of the hypotenuse (c), use the formula: c = √(a² + b²), where a and b are the lengths of the other two sides.

Front

What is the area of a square with a side length of 6 cm?

Back

Area = 6 cm × 6 cm = 36 cm².

Front

If the area of a square is 144 in², what is the length of one side?

Back

Length of one side = √144 in² = 12 in.

Front

In a right triangle, if one side is 3 units and the other side is 4 units, what is the length of the hypotenuse?

Back

Hypotenuse = √(3² + 4²) = √(9 + 16) = √25 = 5 units.

Front

What is the distance formula derived from the Pythagorean Theorem?

Back

The distance between two points (x₁, y₁) and (x₂, y₂) is given by: Distance = √((x₂ - x₁)² + (y₂ - y₁)²).

Front

If John walks 6 blocks North and 8 blocks West, how far is he from the starting point?

Back

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