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

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 144 in², what is the length of one side?

Back

The length of one side is 12 inches, since side = √(Area) = √(144) = 12.

Front

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

Back

In a Pythagorean Theorem problem, the area of the square on the hypotenuse is equal to the sum of the areas of the squares on the other two sides.

Front

If the area of square A is 25 in² and the area of square B is 169 in², what is the area of square C?

Back

The area of square C is 144 in², since 25 + 169 = 144.

Front

What is the length of the hypotenuse if the lengths of the other two sides are 5 ft and 12 ft?

Back

The length of the hypotenuse is 13 ft, calculated using the Pythagorean Theorem: c = √(5² + 12²) = √(25 + 144) = √169 = 13.

Front

What is the area of a square with a side length of 6.7 cm?

Back

The area is 44.89 cm², calculated as Area = side² = 6.7² = 44.89.

Front

If the area of square B is 144 ft² and the length of side A is 5 ft, what is the area of square C?

Back

The area of square C is 169 ft², since 5² + 12² = 144 + 25 = 169.

Front

What is the length of the longest side of a right triangle with sides 6 cm and 8 cm?

Back

The length of the longest side (hypotenuse) is 10 cm, calculated using the Pythagorean Theorem: c = √(6² + 8²) = √(36 + 64) = √100 = 10.

Front

What is the area of a square with a side length of 15 cm?

Back

The area is 225 cm², calculated as Area = side² = 15² = 225.