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

If one leg of a right triangle is 8 and the other leg is 12, what is the length of the hypotenuse?

Back

Using the Pythagorean Theorem: c² = 8² + 12² = 64 + 144 = 208. Therefore, c = √208 ≈ 14.4.

Front

What is a right triangle?

Back

A right triangle is a triangle that has one angle measuring 90 degrees.

Front

In a right triangle, if the legs are 6 feet and 8 feet, what is the length of the hypotenuse?

Back

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

Front

What is the formula to find the length of the diagonal of a rectangle?

Back

The length of the diagonal (d) can be found using the formula: d = √(length² + width²).

Front

If a ladder is 13 feet long and its base is 5 feet away from the wall, how high does it reach on the wall?

Back

Using the Pythagorean Theorem: c² = 13² = 5² + h². Therefore, h = √(13² - 5²) = √(169 - 25) = √144 = 12 feet.

Front

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

Back

In a right triangle, the sum of the squares of the two legs equals the square of the hypotenuse.

Front

How do you find the length of a side in a right triangle if you know the lengths of the other two sides?

Back

You can use the Pythagorean Theorem: c² = a² + b², where c is the hypotenuse and a and b are the legs.

Front

What is the length of the diagonal of a soccer field that is 90 meters wide and 120 meters long?

Back

Using the formula: d = √(120² + 90²) = √(14400 + 8100) = √22500 = 150 meters.

Front

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

Back

The Pythagorean Theorem is used in various fields such as construction, navigation, and physics to calculate distances and angles.