Pythagorean Theorem Word Problems Practice Challenge

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 height of a ladder leaning against a wall?

Back

To find the height (h) the ladder reaches on the wall, use the Pythagorean Theorem: h = √(c² - a²), where c is the length of the ladder and a is the distance from the base of the ladder to the wall.

Front

What is the formula to calculate the diagonal of a rectangle?

Back

The diagonal (d) of a rectangle can be calculated using the formula: d = √(length² + width²).

Front

How do you find the diagonal distance in a square?

Back

In a square, the diagonal (d) can be found using the formula: d = side × √2, where 'side' is the length of one side of the square.

Front

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

Back

In a right triangle, the lengths of the sides are related by the Pythagorean Theorem: a² + b² = c², where c is the hypotenuse.

Front

If a ramp is 12 inches tall and 6 feet long, how do you find the horizontal distance?

Back

Use the Pythagorean Theorem: horizontal distance = √(length² - height²). Convert all measurements to the same unit before calculating.

Front

What is the significance of the diagonal in measuring screens?

Back

The diagonal measurement of a screen is important because it gives a standard way to compare the size of screens, regardless of their aspect ratio.

Front

How do you calculate the distance between two corners of a rectangle?

Back

To calculate the distance between two corners of a rectangle, use the formula: distance = √(length² + width²).

Front

What is the height of a ladder that is 12 feet long and 5 feet from the wall?

Back

Using the Pythagorean Theorem: height = √(12² - 5²) = √(144 - 25) = √119 ≈ 10.9 feet.

Front

How do you find the distance from one corner of a swimming pool to the opposite corner?

Back

Use the formula for the diagonal: distance = √(length² + width²). For a pool measuring 50 m by 25 m, distance = √(50² + 25²) = √(2500 + 625) = √3125 ≈ 55.9 m.