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

In a right triangle, which side is referred to as the hypotenuse?

Back

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

Front

What are the legs of a right triangle?

Back

The legs of a right triangle are the two sides that form the right angle.

Front

If one leg of a right triangle is 6 feet and the other leg is 8 feet, what is the length of the hypotenuse?

Back

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

Front

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

Back

In a right triangle, the hypotenuse is always longer than either of the legs.

Front

What is the opposite of squaring a number?

Back

The opposite of squaring a number is taking the square root of that number.

Front

Can side a be the longest side in a right triangle?

Back

No, side a cannot be the longest side in a right triangle; the hypotenuse (side c) is always the longest.

Front

What is the formula to find the length of one leg of a right triangle if the hypotenuse and the other leg are known?

Back

If c is the hypotenuse and b is the known leg, the formula is: a = √(c² - b²).

Front

What is the significance of the Pythagorean Theorem in real-world applications?

Back

The Pythagorean Theorem is used in various real-world applications such as construction, navigation, and physics to determine distances and relationships between different points.

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).