a

These four triangles are all members of the (3,4,5) family.

For example, the triple (6,8,10) is ( 3 x 2, 4 x 2 , 5 x 2).

Even though the last triangle, ( 3√3, 4√3 , 5√3), is a member of the (3,4,5) family, the measures of its sides are not a Pythagorean triplets because they are not whole numbers.

Other common families are

(7,24,25), of which (14,48,50) is another member.

(8,15,17), of which (4, 7.5,8.5) is another member.

There are infinitely many families, including (9,40,41),(11,60,61), (20,21,29)

and (12,35,37), but most are not used very often.

1) Find AB .

By Pythagoras triplets method

(10,24,?) belongs to the (5,12,13) family.

10 = 5 x 2

24 = 12 x 2

So, AB = 13 x 2 = 26

The following problems shows how a knowledge of Pythagoras triplets can be useful even in situations where their applicability is not immediately apparent.

1) Given : The right triangle shown

Find : y

The fraction may complicate our work, we may not wish to complete a long calculation to solve 4

An alternative method is to find a more easily recognized member of the same family. We multiply each side by the denominator of the fraction ,2.

4 x 2 = 8 ; 7½ x 2 ; 2y

Clearly the family is (8,15,17)

∴ 2y = 17

y = 17/2

y = 8½

• Introduction of Pythagorean Theorem

• Converse of Pythagorean Theorem

• Pythagorean Triples

• Application of Pythagorean Theorem

• Proof on Pythagorean Theorem

GMAT

GRE

1st Grade

2nd Grade

3rd Grade

4th Grade

5th Grade

6th Grade

7th grade math

8th grade math

9th grade math

10th grade math

11th grade math

12th grade math

Precalculus

Worksheets

Chapter wise Test

MCQ's

Math Dictionary

Graph Dictionary

Multiplicative tables

Math Teasers

NTSE

Chinese Numbers

CBSE Sample Papers