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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,

(h y p o t e n u s e) 2 = (b a s e) 2 + (p e r p e n d i c u l a r) 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 = 252 ⇒ H 2 = 625

LHS –

⇒ P 2 + B 2 = 242 + 72 ⇒ 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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