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

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) on a coordinate plane, use the formula: Distance = √((x2 - x1)² + (y2 - y1)²). This is derived from the Pythagorean Theorem.

Front

If Jane walks 6 blocks east and Miguel walks 8 blocks north, how do you calculate the distance between their schools?

Back

Use the Pythagorean Theorem: Distance = √(6² + 8²) = √(36 + 64) = √100 = 10 blocks.

Front

What is the hypotenuse in a right triangle?

Back

The hypotenuse is the longest side of a right triangle, opposite the right angle.

Front

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

Back

Using the Pythagorean Theorem: c = √(3² + 4²) = √(9 + 16) = √25 = 5.

Front

How do you round a number to the nearest tenth?

Back

To round a number to the nearest tenth, look at the hundredths place. If it is 5 or greater, round up the tenths place by one. If it is less than 5, keep the tenths place the same.

Front

What is the distance from one corner of a rectangle to the opposite corner?

Back

The distance can be found using the Pythagorean Theorem: Distance = √(length² + width²).

Front

If a pool table is 9 feet long and 5 feet wide, what is the diagonal distance?

Back

Distance = √(9² + 5²) = √(81 + 25) = √106 ≈ 10.3 feet.

Front

What is the formula for the Pythagorean Theorem?

Back

The formula is c² = a² + b², where c is the hypotenuse and a and b are the other two sides.

Front

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

Back

Identify the right triangle formed by the problem, label the sides, and use the Pythagorean Theorem to find the unknown side.