27 36 45 Pythagorean triplet or not
Answers
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:
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.