Question

Which set of integers is NOT a Pythagorean triple and are NOT side lengths of a right triangle?

12, 16, 20
10, 24, 26
14, 48, 50
27, 32, 45

Answer 1

4) 27, 32, 45 is NOT a Pythagorean triplet.

Explanation:

Here the given triangle is a Right Triangle.

Now,a s we know, if a , b are the two sides, and c is the hypotenuse, then:

by PYTHAGORAS THEOREM:

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

Also, Hypotenuse is ALWAYS the longest side in a right triangle.

Consider the given cases, and check for Pythagoras theorem:

1) 12, 16, 20

Here, a = 12, b = 16 and c = 20

a² + b² = (12)² + (16)² = 144+ 256 = 400 = (20)² = (c)²

⇒ a² + b² = (c)²

Hence, 12, 16, 20 is a Pythagorean triplet.

2) 10, 24, 26

Here, a = 10, b = 24 and c = 26

a² + b² = (10)² + (24)² = 100+ 576 = 676 = (26)² = (c)²

⇒ a² + b² = (c)²

Hence, 10, 24, 26 is a Pythagorean triplet.

3) 14, 48, 50

Here, a = 14, b = 48 and c = 50

a² + b² = (14)² + (48)² = 196+ 2304 = 2500 = (50)² = (c)²

⇒ a² + b² = (c)²

Hence, 14, 48, 50 is a Pythagorean triplet.

4) 27, 32, 45

Here, a = 27, b = 32 and c = 45

a² + b² = (27)² + (32)² = 729+ 1024 = 1753 ≠ (45)² = 2025 = (c)²

⇒ a² + b² ≠ (c)²

Hence, 27, 32, 45 is NOT a Pythagorean triplet.

Answer 2

Answer is 27, 32, 45

Explanation:

In the right angle triangle, hypontenous is the longest side.

∴ In each option square of longest side has to be equal to the sum of square of other two side.

We know,
`h^(2) = a^(2) + b^(2)` ( as per pythogorean theorem)

If we check the last option; 27, 32, 45

In the given set of integer, we have longest side as 45

∴ conisdering 45 as hyptenous

Subtituting the value in the formula

⇒
`45^(2) = 27^(2) +32^(2)`

⇒
`2025= 729+1024`

⇒
`2025\\eq 1753`

∴
`LHS\\eq RHS`

Hence, the set of given integer is not a pythagorean triple and are not side length of right angle.