Pythagorean Triples

Front

What is a Pythagorean Triple?

Back

A set of three positive integers a, b, and c, such that a² + b² = c². For example, (3, 4, 5) is a Pythagorean Triple.

Front

What is the formula to find the hypotenuse in a right triangle?

Back

The hypotenuse can be found using the formula c = √(a² + b²), where c is the hypotenuse and a and b are the other two sides.

Front

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

Back

10

Front

What are the first three Pythagorean Triples?

Back

(3, 4, 5), (5, 12, 13), (8, 15, 17).

Front

How can you determine if a set of numbers is a Pythagorean Triple?

Back

Check if a² + b² = c² holds true for the numbers.

Front

Is the set of numbers 15, 20, 25 a Pythagorean Triple?

Back

Yes, because 15² + 20² = 25² (225 + 400 = 625).

Front

What is the value of x if the sides of a right triangle are 6, 8, and x?

Back

10

Front

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

Back

In a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.

Front

If 36 and 48 are the two smaller numbers in a Pythagorean Triple, what is the third number?

Back

60

Front

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

Back

It is used in various fields such as construction, navigation, and physics to calculate distances.