Pythagorean Theorem 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: c² = a² + b².

Front

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

Back

To find the length of the diagonal (d) of a rectangle, use the Pythagorean Theorem: d = √(length² + width²).

Front

If a right triangle has legs of lengths 3 and 4, what is the length of the hypotenuse?

Back

Using the Pythagorean Theorem: c = √(3² + 4²) = √(9 + 16) = √25 = 5.

Front

What is the distance formula derived from the Pythagorean Theorem?

Back

The distance between two points (x1, y1) and (x2, y2) in a coordinate plane is given by: d = √((x2 - x1)² + (y2 - y1)²).

Front

In a right triangle, if one leg is 5 and the hypotenuse is 13, what is the length of the other leg?

Back

Using the Pythagorean Theorem: b = √(c² - a²) = √(13² - 5²) = √(169 - 25) = √144 = 12.

Front

What is a real-world application of the Pythagorean Theorem?

Back

The Pythagorean Theorem can be used to determine the shortest distance between two points, such as finding the distance a person would walk diagonally across a rectangular park.

Front

If a ladder is leaning against a wall and reaches a height of 12 feet while the base is 5 feet away from the wall, how long is the ladder?

Back

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

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, where the shortest side is opposite the 30° angle.

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

How can you determine if a triangle is a right triangle using the Pythagorean Theorem?

Back

To determine if a triangle with sides a, b, and c (where c is the longest side) is a right triangle, check if a² + b² = c².