Pythagorean Theorem

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

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

Back

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

Front

What is the length of the other leg if the hypotenuse is 13 cm and one leg is 5 cm?

Back

Using the Pythagorean Theorem: 13² = 5² + b². Thus, 169 = 25 + b², which means b² = 144. Therefore, b = √144 = 12 cm.

Front

What does 'hypotenuse' mean?

Back

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

Front

What is the relationship between the areas of the squares on the sides of a right triangle according to the Pythagorean Theorem?

Back

The area of the square on the hypotenuse is equal to the sum of the areas of the squares on the other two sides.

Front

If a right triangle has legs of lengths 9 cm and 12 cm, what is the area of the square on the hypotenuse?

Back

Using the Pythagorean Theorem: c² = 9² + 12² = 81 + 144 = 225. The area of the square on the hypotenuse is 225 cm².

Front

What is the formula to find the length of a leg if the hypotenuse and the other leg are known?

Back

If c is the hypotenuse and a is the known leg, the formula is: b = √(c² - a²).

Front

In a right triangle, if the hypotenuse is 10 cm and one leg is 6 cm, what is the length of the other leg?

Back

Using the formula: b = √(10² - 6²) = √(100 - 36) = √64 = 8 cm.

Front

What is the significance of the Pythagorean Theorem in real life?

Back

The Pythagorean Theorem is used in various fields such as construction, navigation, and physics to calculate distances and create right angles.

Front

What is a right triangle?

Back

A right triangle is a triangle that has one angle measuring 90 degrees.