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: a² + b² = c².

Front

How do you identify the hypotenuse in a right triangle?

Back

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

Front

If one leg of a right triangle is 8 and the hypotenuse is 12, how do you find the other leg?

Back

Use the Pythagorean Theorem: a² + b² = c². Here, a = 8 and c = 12. So, b² = 12² - 8² = 144 - 64 = 80. Therefore, b = √80 ≈ 8.9.

Front

What is the formula to find the distance across the diagonal of a square?

Back

The distance across the diagonal (d) of a square with side length (s) can be found using the formula: d = s√2.

Front

In a right triangle, if the legs are 90 feet each, what is the length of the hypotenuse?

Back

Using the Pythagorean Theorem: c = √(90² + 90²) = √(8100 + 8100) = √16200 = 90√2 ≈ 127.3 feet.

Front

How do you calculate the diagonal distance of a rectangle?

Back

For a rectangle with length (l) and width (w), the diagonal (d) can be calculated using the formula: d = √(l² + w²).

Front

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

Back

The Pythagorean Theorem establishes a relationship between the lengths of the sides of a right triangle, allowing you to calculate the length of one side if the lengths of the other two sides are known.

Front

If a ladder is 13 feet long and is placed 5 feet away from a wall, how high does it reach?

Back

Using the Pythagorean Theorem: height = √(13² - 5²) = √(169 - 25) = √144 = 12 feet.

Front

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

Back

The Pythagorean Theorem is used in various real-life applications such as construction, navigation, and physics to determine distances and angles.

Front

How can you visualize the Pythagorean Theorem?

Back

You can visualize the Pythagorean Theorem by drawing a right triangle and creating squares on each of the three sides. The area of the square on the hypotenuse equals the sum of the areas of the squares on the other two sides.