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

Back

The length of one side is 5 inches, since 5² = 25.

Front

What is the relationship between the areas of the squares in a Pythagorean Theorem model?

Back

The area of the square on the hypotenuse (c²) is equal to the sum of the areas of the squares on the other two sides (a² + b²).

Front

If a = 5 and b = 12, what is the length of the hypotenuse (c)?

Back

Using the Pythagorean Theorem: c = √(5² + 12²) = √(25 + 144) = √169 = 13.

Front

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

Back

The area is 36 cm², since 6² = 36.

Front

Which equation represents a right triangle with sides 3, 4, and 5?

Back

The equation is 3² + 4² = 5², which simplifies to 9 + 16 = 25.

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.

Front

What is the length of the sides of a right triangle if the sides are 10, 24, and 26?

Back

The sides of the right triangle are 10, 24, and 26.

Front

What is the area of a square if a = 5 and b = 7?

Back

The area of square c is 74, since c² = a² + b² = 5² + 7² = 25 + 49 = 74.