FIND UNKNOWN IN PYTHAGOREAN TRIAPLES

The set of numbers {3, 4, 5} is called Pythagorean triple since it obeys the rule

c2 = a2 + b2

52 = 32 + 42

25 = 9 + 16

25 = 25

Where a, b and c are integers.

Find k given that the following are Pythagorean triples :

Problem 1 :

{9, k, 15}

Solution :

{9, k, 15}

92 + k2 = (15)2

k2 = (15)2 - 92

k2 = 225 – 81

k2 = 144

Take square root of both sides, we get

k =√144

k = 12

So, {9, k, 15} is a Pythagorean triple.

Problem 2 :

{8, 15, k}

Solution :

{8, 15, k}

82 +(15)2 = k2

64 + 225 = k2

289 = k2

Take square root of both sides, we get

k =√289

k = 17

Problem 3 :

{k, 24, 26}

Solution :

{k, 24, 26}

k+ (24)2 = (26)2

k2 = (26)2 – (24)2

k2 = 676 – 576

k2 = 100

Take square root of both sides, we get

k =√100

k = 10

So, {k, 24, 26} is a Pythagorean triple.

Problem 4 :

{11, k, 61}

Solution :

{11, k, 61}

(11)2 + k2 = (61)2

k2 = (61)2 – (11)2

k2 = 3721 – 121

k2 = 3600

Take square root of both sides, we get

k =√3600

k = 60

How to Check If the Given Numbers are Pythagorean Triples

Check if the following sets of numbers form Pythagorean triples?

Problem 5 :

{3, 7, 9}

Solution :

{3, 7, 9}

32 + 72 = 92

9 + 49 = 81

58 = 81

So, {3, 7, 9} is not a Pythagorean triple.

Problem 6 :

{14, 48, 50}

Solution :

{14, 48, 50}

(14)2 + (48)2 = (50)2

196 + 2304 = 2500

2500 = 2500

So, {3, 7, 9} is a Pythagorean triple.

Problem 7 :

{7.5, 10, 12.5}

Solution :

{7.5, 10, 12.5}

(7.5)2 + (10)2 = (12.5)2

56.25 + 100 = 156.25

156.25 = 156.25

So, {7.5, 10, 12.5} is a Pythagorean triple.

Problem 8 :

{5, 12, 13}

Solution :

{5, 12, 13}

52 + (12)2 = (13)2

25 + 144 = 169

169 = 169

So, {5, 12, 13} is a Pythagorean triple.

Problem 9 :

{7, 24, 25}

Solution :

{7, 24, 25}

72 + (24)2 = (25)2

49 + 576 = 625

625 = 625

So, {7, 24, 25} is a Pythagorean triple.

Problem 10 :

{8, 15, 17}

Solution :

{8, 15, 17}

82 + (15)2 = (17)2

64 + 225 = 289

289 = 289

So, {8, 15, 17} is a Pythagorean triple. 

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