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 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. 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 do you apply the Pythagorean Theorem to real-world problems?

Back

Identify the right triangle in the problem, label the sides, and use the Pythagorean Theorem to find the unknown side.

Front

What is the significance of the Pythagorean Theorem in geometry?

Back

The Pythagorean Theorem is fundamental in geometry as it relates the lengths of sides in right triangles and is used in various applications, including construction and navigation.

Front

If a ladder is leaning against a wall, how can you use the Pythagorean Theorem to find the height it reaches?

Back

If the base of the ladder is a distance 'b' from the wall and the ladder length is 'c', the height 'h' can be found using: h = √(c² - b²).