determime if a triangle with sides 9cm , 12cm and 15cm is a right angke triangle
Answers
Answer: Yes it is a right angled triangle.
Step-by-step explanation:
In a right angled triangle, the longest side, which is the hypotenuse is equal to the square root of the sum of squares of the other two sides, that is it follows Pythagoras theorem.
Here,
9^2= 81
12^2= 144
15^2=225
Therefore,
12^2+9^2 = 144+81= 225 = 15^2
Therefore it is a right angled triangle.
Hope this helps.
We know that,
The sides of a right angle triangle are Pythagorean triplets.
Means, the square of the longest side (hypotenuse) is equal to the sum of the square of other two sides.
Here, the longest side is 15cm.
Let us consider the triangle is right angle triangle where hypotenuse is 15cm. and other two sides (base and perpendicular)
VERIFICATION :-
LHS :-
= hypotenuse²
= 15²
= 225
RHS :-
= 9² + 12²
= 81 + 144
= 225
LHS = RHS. Hence it's a Pythagorean triplet and i.e The triangle is a right angle triangle.