Pythagorean Theorem 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 is expressed as a² + b² = c².

Front

In a right triangle, which side is the hypotenuse?

Back

The hypotenuse is the longest side of a right triangle, opposite the right angle.

Front

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

Back

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

Front

What is the formula to find the length of a side in a right triangle using the Pythagorean Theorem?

Back

To find the length of a side, rearrange the Pythagorean Theorem: a² = c² - b² or b² = c² - a².

Front

How do you find the length of the diagonal of a rectangle?

Back

Use the Pythagorean Theorem: if the rectangle has a width (a) and height (b), the diagonal (d) is found using d = √(a² + b²).

Front

What is the relationship between the sides of a 30-60-90 triangle?

Back

In a 30-60-90 triangle, the lengths of the sides are in the ratio 1:√3:2.

Front

What is the relationship between the sides of a 45-45-90 triangle?

Back

In a 45-45-90 triangle, the lengths of the legs are equal, and the hypotenuse is √2 times the length of each leg.

Front

If a ladder is placed 10 feet away from a wall and reaches a height of 27 feet, how long is the ladder?

Back

The ladder is 27 feet long (using the Pythagorean Theorem: 10² + 27² = 100 + 729 = 829; √829 ≈ 28.8 feet).

Front

What is the length of the diagonal of a piece of paper that is 11 inches tall and 8 inches wide?

Back

The diagonal is approximately 13.6 inches (using the Pythagorean Theorem: √(11² + 8²) = √(121 + 64) = √185 ≈ 13.6).

Front

If a right triangle has a hypotenuse of 13 and one side of 5, what is the length of the other side?

Back

The other side is 12 (using the Pythagorean Theorem: 5² + b² = 13²; 25 + b² = 169; b² = 144; b = 12).