Pythagorean Theorem Practice with Word Problems

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 type of triangle does the Pythagorean Theorem apply to?

Back

The Pythagorean Theorem ONLY works on right triangles.

Front

If one side of a right triangle is 3 cm and the other side is 4 cm, what is the length of the hypotenuse?

Back

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

Front

What is the length of the diagonal of a rectangle that is 8 inches wide and 6 inches tall?

Back

10 inches (using the Pythagorean Theorem: 8² + 6² = 64 + 36 = 100; √100 = 10).

Front

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

Back

5 cm (using the Pythagorean Theorem: 12² + b² = 13²; 144 + b² = 169; b² = 25; b = 5).

Front

What is the distance from the top of a 10-foot ladder leaning against a wall if the base is 6 feet away from the wall?

Back

8 feet (using the Pythagorean Theorem: 6² + h² = 10²; 36 + h² = 100; h² = 64; h = 8).

Front

If a right triangle has legs of lengths 5 cm and 12 cm, what is the area of the triangle?

Back

30 cm² (Area = 1/2 * base * height = 1/2 * 5 * 12).

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.

Front

If a right triangle has a hypotenuse of 15 cm and one leg of 9 cm, what is the length of the other leg?

Back

12 cm (using the Pythagorean Theorem: 9² + b² = 15²; 81 + b² = 225; b² = 144; b = 12).

Front

What is the formula to find the length of the hypotenuse in a right triangle?

Back

c = √(a² + b²), where c is the hypotenuse and a and b are the other two sides.