Pythagorean Theorem Models

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

If a = 3 cm and b = 4 cm, what is the length of c?

Back

c = 5 cm (using the Pythagorean Theorem: 3² + 4² = 9 + 16 = 25, so c = √25 = 5).

Front

What is the area of a square with side length 5 ft?

Back

The area of a square is calculated as side length squared. Therefore, area = 5 ft × 5 ft = 25 ft².

Front

If the area of square b is 144 ft², what is the length of side b?

Back

The length of side b is 12 ft (since area = side², √144 = 12).

Front

What is the relationship between the areas of squares in a right triangle?

Back

The area of the square on the hypotenuse (c) is equal to the sum of the areas of the squares on the other two sides (a and b).

Front

If the area of square c is 225 cm², what is the length of side c?

Back

The length of side c is 15 cm (since area = side², √225 = 15).

Front

What is the area of a square with side length 12 cm?

Back

The area is 144 cm² (12 cm × 12 cm = 144 cm²).

Front

If a = 5 cm and b = 12 cm, what is the area of square c?

Back

The area of square c is 169 cm² (using the Pythagorean Theorem: c² = 5² + 12² = 25 + 144 = 169).

Front

What is the formula to find the area of a square?

Back

Area = side length × side length (or side²).

Front

If the area of the blue square is 25 in² and the area of the green square is 169 in², what is the area of the yellow square?

Back

The area of the yellow square is 144 in² (169 in² - 25 in² = 144 in²).