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 diagonal of a rectangle?

Back

To find the length of the diagonal (d) of a rectangle, use the Pythagorean Theorem: d = √(width² + height²).

Front

If a television screen is 3 feet tall and 6 feet wide, what is the size of the screen?

Back

The size of the screen is approximately 6.7 feet, calculated using the Pythagorean Theorem: d = √(3² + 6²) = √(9 + 36) = √45 ≈ 6.7.

Front

How do you determine the distance from the base of a building when using a zipline?

Back

Use the Pythagorean Theorem. If the height of the building is 80 feet and the length of the zipline is 100 feet, the distance from the base (x) can be found using: 100² = 80² + x².

Front

What is the distance formula derived from the Pythagorean Theorem?

Back

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

Front

An airplane flies 56 miles north and 33 miles east. How do you find the distance from the starting point?

Back

Use the Pythagorean Theorem: d = √(56² + 33²) = √(3136 + 1089) = √4225 = 65 miles.

Front

How tall does a ladder need to be to reach a 25-foot tall house when placed 10 feet away?

Back

Use the Pythagorean Theorem: c² = 10² + 25², so c = √(100 + 625) = √725 ≈ 27 feet.

Front

What is a right triangle?

Back

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

Front

What is the hypotenuse in a right triangle?

Back

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

Front

What is the relationship between the sides of a 3-4-5 triangle?

Back

In a 3-4-5 triangle, the lengths of the sides are in the ratio 3:4:5, which satisfies the Pythagorean Theorem: 5² = 3² + 4².