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 can you determine if a triangle is a right triangle using side lengths?

Back

To determine if a triangle is a right triangle, check if the square of the longest side is equal to the sum of the squares of the other two sides. If a² + b² = c² holds true, then the triangle is a right triangle.

Front

What is the relationship between the sides of a right triangle and the lengths of the ladder and wall in a word problem?

Back

In a word problem involving a ladder leaning against a wall, the ladder acts as the hypotenuse of a right triangle, while the height of the wall and the distance from the wall to the base of the ladder represent the other two sides.

Front

How do you calculate the height of a ladder needed to reach a certain height when placed a specific distance away?

Back

Use the Pythagorean Theorem: c² = a² + b², where c is the length of the ladder, a is the height of the wall, and b is the distance from the wall to the base of the ladder.

Front

What is the formula to find the diagonal of a rectangle given its width and height?

Back

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

Front

In a right triangle, if one side is 12 feet and the other side is 9 feet, what is the length of the hypotenuse?

Back

Using the Pythagorean Theorem: c = √(12² + 9²) = √(144 + 81) = √225 = 15 feet.

Front

What is the significance of the 3-4-5 triangle in relation to the Pythagorean Theorem?

Back

The 3-4-5 triangle is a common example of a right triangle where the sides are in a ratio that satisfies the Pythagorean Theorem (3² + 4² = 5²). It is often used as a quick reference for determining right angles.

Front

How do you find the distance between two points using the Pythagorean Theorem?

Back

To find the distance between two points (x1, y1) and (x2, y2) in a coordinate plane, use the formula: distance = √((x2 - x1)² + (y2 - y1)²).

Front

What is the relationship between the sides of a right triangle and the lengths of the sides in a word problem involving walking distances?

Back

In a word problem involving walking distances, the two walking paths can represent the two legs of a right triangle, while the direct distance across represents the hypotenuse.

Front

How do you apply the Pythagorean Theorem to real-world problems?

Back

To apply the Pythagorean Theorem to real-world problems, identify the right triangle formed by the scenario, label the sides, and use the theorem to solve for the unknown side.