Question

27 36 45 Pythagorean triplet or not

Answer 1

Answer:

yes 27 36 and 45 is a Pythagorean triplets

Step-by-step explanation:

Pythagoras theoram

asquare plus bsquare equals csquare

here

• asquare is 27*27 = 729
• bsquare is 36*36= 1296
• csquare is 45*45=2025

729+1297=2025

hence they are Pythagorean triplets

Answer 2

Answer:

Yes, ( 27, 36, 45 ) is a Pythagorean triplet.

Step-by-step-explanation:

We have given a triplet.

We have to decide whether it is a Puthagorean triplet or not.

The given triplet is ( 27, 36, 45 ).

The greatest side of the triangle is 45.

∴ Hypotenuse of the triangle = 45 units

Now,

Side₁ = 27 units

Side₂ = 36 units

Now,

( Hypotenuse )² = ( 45 )²

⇒ ( Hypotenuse )² = 45 * 45

⇒ ( Hypotenuse )² = 2025 - - ( 1 )

Now, by adding squares of other sides, we get,

( Side₁ )² + ( Side₂ )² = ( 27 )² + ( 36 )²

⇒ ( Side₁ )² + ( Side₂ )² = ( 27 * 27 ) + ( 36 * 36 )

⇒ ( Side₁ )² + ( Side₂ )² = 729 + 1296

⇒ ( Side₁ )² + ( Side₂ )² = 2025 - - ( 2 )

Now, from equations ( 1 ) & ( 2 ), we get,

( Hypotenuse )² = ( Side₁ )² + ( Side₂ )²

∴ By converse of Pythagoras theorem,

( 27, 36, 45 ) is a Pythagorean triplet.

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Additional Information:

1. Pythagoras Theorem:

This theorem is given by mathematician Pythagoras.

It states the relation between the sides of a right angled triangle.

In a right angled triangle, the square of hypotenuse is equal to the sum of squares of the remaining two sides.

2. Converse of Pythagoras theorem:

It is the inverse of the Pythagoras theorem.

If the square of hypotenuse is equal to the sum of squares of the remaining two sides, then the triangle is a right angled triangle.