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). Formula: a² + b² = c².

Front

If a = 9 and b = 40, what is c?

Back

c = 41 (Using the Pythagorean Theorem: 9² + 40² = c² => 81 + 1600 = c² => c² = 1681 => c = 41).

Front

What is the perimeter of a triangle with legs 3 cm and 4 cm?

Back

The perimeter is 12 cm (3 + 4 + 5 = 12, where 5 is the hypotenuse calculated using the Pythagorean Theorem).

Front

Find the length of the missing side if one side is 80 in and the other is 60 in.

Back

The missing side is 100 in (Using the Pythagorean Theorem: 80² + 60² = c² => 6400 + 3600 = c² => c² = 10000 => c = 100).

Front

How tall does a ladder need to be to reach a 25-foot tall house when placed 10 feet away?

Back

The ladder needs to be 27 feet tall (Using the Pythagorean Theorem: 10² + 25² = c² => 100 + 625 = c² => c² = 725 => c ≈ 27).

Front

What is the hypotenuse of a right triangle with legs of 6 cm and 8 cm?

Back

The hypotenuse is 10 cm (Using the Pythagorean Theorem: 6² + 8² = c² => 36 + 64 = c² => c² = 100 => c = 10).

Front

If one leg of a right triangle is 12 and the hypotenuse is 13, what is the length of the other leg?

Back

The other leg is 5 (Using the Pythagorean Theorem: 12² + b² = 13² => 144 + b² = 169 => b² = 25 => b = 5).

Front

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

Back

In a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides (a² + b² = c²).

Front

What is the formula to calculate the area of a right triangle?

Back

Area = 1/2 * base * height (where base and height are the two legs of the triangle).

Front

If a right triangle has legs of 9 and 12, what is the length of the hypotenuse?

Back

The hypotenuse is 15 (Using the Pythagorean Theorem: 9² + 12² = c² => 81 + 144 = c² => c² = 225 => c = 15).