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 = √(width² + length²).

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 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 determine if a triangle is a right triangle using the Pythagorean Theorem?

Back

To determine if a triangle is a right triangle, check if the square of the longest side equals the sum of the squares of the other two sides (c² = a² + b²).

Front

What is the formula to calculate the height of a ladder leaning against a wall?

Back

The height (h) of the ladder can be found using the Pythagorean Theorem: h = √(ladder length² - distance from wall²).

Front

If a ladder is 10 feet long and placed 6 feet away from the wall, how high does it reach?

Back

Using the formula: h = √(10² - 6²) = √(100 - 36) = √64 = 8 feet.

Front

What is the formula for the diagonal of a rectangle with width w and height h?

Back

The diagonal (d) can be calculated using: d = √(w² + h²).

Front

How do you find the distance between two points in a coordinate plane?

Back

Use the distance formula: d = √((x2 - x1)² + (y2 - y1)²).