Question

For each pair of numbers, find a third whole number such that the three numbers form a pythagorean triple.

33,55
42,58
60,65

Answer 1

Part 1) The third whole number is 44

Part 2) The third whole number is 40

Part 3) The third whole number is 25

Explanation:

we know that

The Pythagoras theorem states that

In a right triangle

`c^(2) =a^(2) +b^(2)`

where

c is the greater length side

a and b are the legs

Case 1) we have

33,55

step a

Let

`a=33, b=55`

Find the value of c

`c^(2) =a^(2) +b^(2)`

`c^(2) =33^(2) +55^(2)`

`c^(2) =4,114`

`c =64.14` ------> is not a whole number

step b

Let

`a=33, c=55`

Find the value of b

`b^(2) =c^(2) -a^(2)`

`b^(2) =55^(2) -33^(2)`

`b^(2) =1,936`

`b=44`

Case 2) we have

42,58

step a

Let

`a=42, b=58`

Find the value of c

`c^(2) =a^(2) +b^(2)`

`c^(2) =42^(2) +58^(2)`

`c^(2) =5,128`

`c =71.61` ------> is not a whole number

step b

Let

`a=42, c=58`

Find the value of b

`b^(2) =c^(2) -a^(2)`

`b^(2) =58^(2) -42^(2)`

`b^(2) =1,600`

`b=40`

Case 3) we have

60,65

step a

Let

`a=60, b=65`

Find the value of c

`c^(2) =a^(2) +b^(2)`

`c^(2) =60^(2) +65^(2)`

`c^(2) =7,825`

`c =88.46` ------> is not a whole number

step b

Let

`a=60, c=65`

Find the value of b

`b^(2) =c^(2) -a^(2)`

`b^(2) =65^(2) -60^(2)`

`b^(2) =625`

`b=25`