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). This can be expressed as: a² + b² = c².

Front

What type of triangle does the Pythagorean Theorem apply to?

Back

The Pythagorean Theorem only applies to right triangles.

Front

In the equation a² + b² = c², what does 'c' represent?

Back

'c' represents the length of the hypotenuse, which is the side opposite the right angle in a right triangle.

Front

If one side of a right triangle is 6 meters and the other side is 8 meters, what is the length of the hypotenuse?

Back

Using the Pythagorean Theorem: c² = 6² + 8² = 36 + 64 = 100. Therefore, c = √100 = 10 meters.

Front

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

Back

In a right triangle, the hypotenuse is always the longest side, and it is opposite the right angle.

Front

How do you find the length of a side in a right triangle if you know the lengths of the other two sides?

Back

You can use the Pythagorean Theorem: a² + b² = c², where you can solve for the unknown side.

Front

What is the distance a ladder reaches against a wall if it is 13 meters long and the base is 5 meters away from the wall?

Back

Using the Pythagorean Theorem: a² + 5² = 13². Therefore, a² = 169 - 25 = 144, so a = √144 = 12 meters.

Front

What is the formula to calculate the diagonal distance across a rectangle?

Back

The diagonal distance (d) across a rectangle can be calculated using the Pythagorean Theorem: d² = length² + width².

Front

In a right triangle, if one side is 9 meters and the hypotenuse is 15 meters, how do you find the other side?

Back

Use the Pythagorean Theorem: a² + 9² = 15². Therefore, a² = 225 - 81 = 144, so a = √144 = 12 meters.

Front

What is the significance of the right angle in a right triangle?

Back

The right angle (90 degrees) is crucial because it allows the use of the Pythagorean Theorem to relate the lengths of the sides.