Extra Practice 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

In a right triangle, what are the legs?

Back

The legs of a right triangle are the two sides that form the right angle. They are usually referred to as 'a' and 'b' in the Pythagorean Theorem.

Front

If one leg of a right triangle is 12 feet and the other leg is 9 feet, what is the length of the hypotenuse?

Back

Using the Pythagorean Theorem: c² = 12² + 9² = 144 + 81 = 225. Therefore, c = √225 = 15 feet.

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 formula: d = √(length² + width²).

Front

What is the area of a rectangle with a length of 10 inches and a width of 5 inches?

Back

The area (A) of a rectangle is calculated as: A = length × width. So, A = 10 inches × 5 inches = 50 square inches.

Front

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

Back

In a right triangle, the relationship between the sides is defined by the Pythagorean Theorem, which states that the square of the hypotenuse is equal to the sum of the squares of the other two sides.

Front

If a ladder is placed 9 feet from the base of a wall and reaches a height of 12 feet, what is the length of the ladder?

Back

Using the Pythagorean Theorem: c² = 12² + 9² = 144 + 81 = 225. Therefore, the length of the ladder (c) is √225 = 15 feet.

Front

What is the formula for the area of a triangle?

Back

The area (A) of a triangle is calculated as: A = 1/2 × base × height.

Front

If the height of a slide is 6 feet and the base is 8 feet, what is the length of the slide?

Back

Using the Pythagorean Theorem: c² = 6² + 8² = 36 + 64 = 100. Therefore, the length of the slide (c) is √100 = 10 feet.

Front

What is the length of the diagonal of a rectangle that is 11 inches tall and 8 inches wide?

Back

Using the formula for the diagonal: d = √(11² + 8²) = √(121 + 64) = √185 ≈ 13.6 inches.