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Q.

State True or False.
If the sides of a triangle are 7cm, 24cm and 25cm. Then the given triangle is a right triangle.
 


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a

True

b

False 

answer is A.

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Detailed Solution

Given that the sides of a triangle are 7cm, 24cm and 25cm.
We know that for a triangle to be right-angled triangle, it should satisfy Pythagoras theorem.
Pythagoras theorem states that in a right-angled triangle,
(hypotenuse) 2 = (base) 2 + (perpendicular) 2  .
So, the largest side is considered to be the hypotenuse.
Let us verify the theorem for the given triangle.
Here, according to given values,
H = 25cm and let P = 7cm and B = 24 cm.
Now using Pythagoras theorem, we have
P 2 + B 2 = H 2  
RHS –
⇒ H 2 = 25 2 ⇒ H 2 =625  
LHS –
⇒ P 2 + B 2 = 24 2 + 7 2 ⇒ P 2 + B 2 =576+49 ⇒ P 2 + B 2 =625  
Since LHS = RHS, it is a right-angled triangle.
The given statement is true.
Therefore, the correct answer is 1.

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State True or False.If the sides of a triangle are 7cm, 24cm and 25cm. Then the given triangle is a right triangle.