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 hypotenuse in a right triangle?

Back

To find the length of the hypotenuse, use the Pythagorean Theorem: c = √(a² + b²), where c is the hypotenuse and a and b are the lengths of the other two sides.

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 a real-world application of the Pythagorean Theorem?

Back

The Pythagorean Theorem can be used to determine the distance between two points in a coordinate system, such as finding the shortest path between two locations.

Front

How do you solve a word problem involving the Pythagorean Theorem?

Back

Identify the right triangle in the problem, assign values to the legs, and use the Pythagorean Theorem to find the unknown side.

Front

In a right triangle, if one leg is 6 and the hypotenuse is 10, what is the length of the other leg?

Back

Using the Pythagorean Theorem: b = √(10² - 6²) = √(100 - 36) = √64 = 8.

Front

What is the distance formula derived from the Pythagorean Theorem?

Back

The distance formula is d = √((x₂ - x₁)² + (y₂ - y₁)²), which calculates the distance between two points (x₁, y₁) and (x₂, y₂) in a plane.

Front

If a pool table is 9 feet long and 5 feet wide, how far is it from one corner pocket to the diagonally opposite corner pocket?

Back

Using the Pythagorean Theorem: c = √(9² + 5²) = √(81 + 25) = √106 ≈ 10.29 feet.

Front

In a right triangle, if one leg is 2 miles and the other leg is 4 miles, what is the length of the hypotenuse?

Back

Using the Pythagorean Theorem: c = √(2² + 4²) = √(4 + 16) = √20 ≈ 4.47 miles.

Front

Lisa drives her car 46 km south and then 13 km east. How far is she from her starting point?

Back

Using the Pythagorean Theorem: d = √(46² + 13²) = √(2116 + 169) = √2285 ≈ 47.80 km.