Question

Which of the following is not a Pythagorean triplet?
a) (15,8,17) b) (5,12,13) c) (3,4,5) d) (15,7,18)

Answer 1

Answer:

d

Step-by-step explanation:

Pythagorean triples are a2+b2 = c2 where a, b and c are the three positive integers. These triples are represented as (a,b,c). Here, a is the perpendicular, b is the base and c is the hypotenuse of the right-angled triangle. The most known and smallest triplets are (3,4,5) (5,12,13) (8,15,17)

When each term in these triplet are multiplied by any number then the numbers formed are also pythagorean triplet.

eg. 3×2, 4×2, 5×2 = (6,8,10) is a famous pythagorean triplet

also, 5×2, 12×2, 13×2 = (10,24,26) is also a used pythagorean triplet

so the correct answer is d as rest are pythagoren triplets but d is not

Answer 2

Given:

a) (15,8,17) b) (5,12,13) c) (3,4,5) d) (15,7,18)

To Find:

Which of the following is not a Pythagorean triplet?

Solution:

For three numbers to be a Pythagorean triplet the square of the largest number needs to be the sum of the square of the other two numbers, let's say if there is a,b,c numbers where a>b,c then for them to be a Pythagorean triplet the below condition needs to be satisfied,

$a^2=b^2+c^2$

(a) (15,8,17)

$17^2=15^2+8^2\\289=225+64\\289=289$

Hence, it is a Pythagorean triplet.

(b) (5,12,13)

$13^2=12^2+5^2\\169=144+25\\169=169$

Hence, it is a Pythagorean triplet.

(c) (3,4,5)

$5^2=4^2+3^2\\25=16+9\\25=25$

Hence, it is a Pythagorean triplet.

(d) (15,7,18)

$18^2=15^2+7^2\\324=225+49\\324\neq 274$

Hence, it is not a Pythagorean triplet

Hence, Of the following triplets (15,7,18) is not Pythagorean triplet.