Pythagorean Triples

Front

What is a Pythagorean Triple?

Back

A set of three positive integers a, b, and c that satisfy the equation a² + b² = c².

Front

Give an example of a Pythagorean Triple.

Back

(3, 4, 5) is a classic example of a Pythagorean Triple.

Front

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

Back

Check if the sum of the squares of the two smaller numbers equals the square of the largest number.

Front

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

Back

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).

Front

If a triangle has sides of lengths 4, 5, and 6, what type of triangle is it?

Back

It is an acute triangle.

Front

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

Back

c = √(a² + b²) where c is the hypotenuse and a and b are 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

Solve for c if a = 5 and b = 12.

Back

c = 13.

Front

Find the value of x in the equation 8² + x² = 10².

Back

x = 6.

Front

What is the smallest Pythagorean Triple?

Back

(3, 4, 5) is the smallest Pythagorean Triple.