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

How do you find the length of the diagonal of a square?

Back

To find the length of the diagonal (d) of a square with side length (s), use the formula: d = s√2.

Front

If a square has an area of 81 square centimeters, what is the length of one side?

Back

The length of one side (s) can be found by taking the square root of the area: s = √81 = 9 cm.

Front

What is the distance formula derived from the Pythagorean Theorem?

Back

The distance (d) 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 determine if a triangle is acute, right, or obtuse using side lengths?

Back

Use the Pythagorean Theorem: If a² + b² = c², the triangle is right; if a² + b² > c², it is acute; if a² + b² < c², it is obtuse.

Front

What is the height of a right triangle if the base is 8 feet and the hypotenuse is 10 feet?

Back

Using the Pythagorean Theorem: h² + 8² = 10²; h² + 64 = 100; h² = 36; h = 6 feet.

Front

In a right triangle, if one leg is 6 feet and the other leg is 8 feet, what is the length of the hypotenuse?

Back

Using the Pythagorean Theorem: c² = 6² + 8²; c² = 36 + 64; c² = 100; c = 10 feet.

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.

Front

How far from the base of a wall should a ladder be placed to reach the top?

Back

Use the Pythagorean Theorem: If the height of the wall is h and the length of the ladder is l, the distance from the wall (d) is found using: d = √(l² - h²).

Front

What is the area of a triangle with a base of 10 meters and a height of 5 meters?

Back

The area (A) of a triangle is given by: A = 1/2 * base * height; A = 1/2 * 10 * 5 = 25 square meters.