Question

verify (8,10,12)is a pythogorean triplet or not​

Answer 1

Answer:

No it is not a pythogorean triplet

Step-by-step explanation:

(8)²+(10)²≠(12)²

64+100≠144

164≠144

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Answer 2

Answer

False.

Things to know

• Pythagorean Triplet

→ Lengths of each side of a right triangle.

• (Converse of) Pythagorean Theorem

→ A right triangle with sides $a,b,c$ forms if $a^2+b^2=c^2$.

Solution

Assume (8, 10, 12) is a Pythagorean triplet. Now let's construct a similar triangle using the SSS postulate.

A triangle with sides 4, 5, 6 must be a right triangle.

But $4^2+5^2\neq 6^2$. A right triangle does not form. Our assumption was wrong.

So (8, 10, 12) is not a Pythagorean triplet.

More information

(a,b,c) is a Pythagorean triplet then (ka, kb, kc) is a Pythagorean triplet. Two triangles are in a similarity ratio of 1:k.

For example, (3, 4, 5) is a Pythagorean triplet. So (6, 8, 10) and (9, 12, 15) will be Pythagorean triplets.