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

Answer:

Answer is 27, 32, 45

Step-by-step 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

⇒$45^{2} = 27^{2} +32^{2}$

⇒$2025= 729+1024$

⇒$2025\neq 1753$

∴ $LHS\neq RHS$

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

Answer 2

Answer:

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

Step-by-step 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.