FIND UNKNOWN IN PYTHAGOREAN TRIAPLES

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}

k² + (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.