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

What is the longest side of a right triangle called?

Back

The longest side of a right triangle is called the hypotenuse.

Front

In a right triangle, which side is always opposite the right angle?

Back

The hypotenuse is always opposite the right angle.

Front

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

Back

Using the Pythagorean theorem: c² = 3² + 4² = 9 + 16 = 25, so c = 5 meters.

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

How do you calculate the distance between two points using the Pythagorean theorem?

Back

To calculate the distance between two points (x1, y1) and (x2, y2), use the formula: distance = √((x2 - x1)² + (y2 - y1)²).

Front

What is the formula for finding the diagonal of a rectangle?

Back

The formula for finding the diagonal (d) of a rectangle with width (w) and length (l) is: d = √(w² + l²).

Front

If a right triangle has legs of lengths 6 and 8, what is the length of the hypotenuse?

Back

Using the Pythagorean theorem: c² = 6² + 8² = 36 + 64 = 100, so c = 10.

Front

What is the significance of the hypotenuse in real-world applications?

Back

The hypotenuse is significant in real-world applications such as construction, navigation, and physics, where direct distances need to be calculated.

Front

What is the relationship between the sides of a right triangle and the angles?

Back

In a right triangle, the side opposite the largest angle is the longest side (hypotenuse), and the side lengths can be used to determine the angles using trigonometric ratios.