Pythagorean Theorem Word Problems Practice

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 diagonal length of a rectangle using the Pythagorean Theorem?

Back

To find the diagonal length (d) of a rectangle, use the formula d = √(width² + height²). This is derived from the Pythagorean Theorem, treating the width and height as the two legs of a right triangle.

Front

If a right triangle has legs of lengths 3 and 4, what is the length of the hypotenuse?

Back

Using the Pythagorean Theorem: c² = 3² + 4² = 9 + 16 = 25. Therefore, c = √25 = 5.

Front

What is the distance formula derived from the Pythagorean Theorem?

Back

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

Front

How do you round a number to the nearest whole number?

Back

To round a number to the nearest whole number, look at the digit to the right of the decimal point. If it is 5 or greater, round up. If it is less than 5, round down.

Front

What is the hypotenuse of a right triangle with legs measuring 5 and 12?

Back

Using the Pythagorean Theorem: c² = 5² + 12² = 25 + 144 = 169. Therefore, c = √169 = 13.

Front

In a right triangle, if one leg is 8 and the hypotenuse is 10, what is the length of the other leg?

Back

Using the Pythagorean Theorem: 10² = 8² + b². Thus, 100 = 64 + b², so b² = 36, and b = √36 = 6.

Front

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

Back

The Pythagorean Theorem is used in various real-life applications such as construction, navigation, and physics to calculate distances and angles.

Front

How can you apply the Pythagorean Theorem to find the length of a ramp?

Back

To find the length of a ramp, treat the vertical height and horizontal length as the two legs of a right triangle, and use the Pythagorean Theorem to find the hypotenuse.

Front

What is the relationship between the sides of a 30-60-90 triangle?

Back

In a 30-60-90 triangle, the lengths of the sides are in the ratio 1:√3:2. The shortest side is opposite the 30° angle, the longer leg is opposite the 60° angle, and the hypotenuse is twice the shortest side.