Pythagorean Triples

Front

What is a Pythagorean Triple?

Back

A Pythagorean Triple consists 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 length of the diagonal in a right triangle?

Back

The length of the diagonal (hypotenuse) can be found using the Pythagorean theorem: 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 feet and the hypotenuse is 10 feet, what is the length of the other side?

Back

8 feet. Using the Pythagorean theorem: 10² = 6² + x², so x = √(100 - 36) = √64 = 8.

Front

What are the first three Pythagorean Triples?

Back

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

Front

How do you determine if three numbers form a Pythagorean Triple?

Back

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

Front

What is the length of the diagonal of a rectangle with sides 120 ft and 160 ft?

Back

200 ft. Using the Pythagorean theorem: c = √(120² + 160²) = √(14400 + 25600) = √40000 = 200.

Front

If a right triangle has legs of length 5 and 12, what is the length of the hypotenuse?

Back

13. Using the Pythagorean theorem: c = √(5² + 12²) = √(25 + 144) = √169 = 13.

Front

What is the relationship between the sides of a 30-60-90 triangle?

Back

In a 30-60-90 triangle, the lengths of the sides are in the ratio 1:√3:2.

Front

What is the missing side if one side is 12 and the hypotenuse is 13?

Back

5. Using the Pythagorean theorem: 13² = 12² + x², so x = √(169 - 144) = √25 = 5.

Front

What is the missing side if one side is 24 and the hypotenuse is 26?

Back

10. Using the Pythagorean theorem: 26² = 24² + x², so x = √(676 - 576) = √100 = 10.