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

What is a right triangle?

Back

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

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

What is the distance between two points in a coordinate plane?

Back

The distance between two points (x1, y1) and (x2, y2) can be found using the distance formula: d = √((x2 - x1)² + (y2 - y1)²).

Front

If one leg of a right triangle is 3 and the other leg is 4, what is the length of the hypotenuse?

Back

Using the Pythagorean Theorem: c = √(3² + 4²) = √(9 + 16) = √25 = 5.

Front

What is the area of a square?

Back

The area of a square is calculated by squaring the length of one of its sides: Area = side².

Front

How do you find the height of a kite using the Pythagorean Theorem?

Back

If the length of the string (hypotenuse) is known and the distance from the person to the point directly below the kite (one leg) is known, use the Pythagorean Theorem to find the height (the other leg).

Front

What is the formula for the area of a right triangle?

Back

The area of a right triangle is given by the formula: Area = (1/2) × base × height.

Front

If the area of one square is 369 and another is 81, what is the area of the missing square?

Back

Using the Pythagorean Theorem: Area of missing square = 369 + 81 = 450.

Front

What is the diagonal of a rectangle?

Back

The diagonal of a rectangle can be found using the Pythagorean Theorem: d = √(width² + height²).