State True or False.
If the sides of a triangle are 13cm, 12cm and 5cm. Then the given triangle is not a right triangle.

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True

False

answer is B.

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Detailed Solution

Given that the sides of a triangle are 13cm, 12cm and 5cm.
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 = 13 cm and let P = 12cm and B = 5 cm.
Now using Pythagoras theorem, we have

P 2 + B 2 = H 2

RHS –

⇒ H 2 = 132 ⇒ H 2 = 169

LHS –

⇒ P 2 + B 2 = 122 + 52 ⇒ P 2 + B 2 = 144 + 25 ⇒ P 2 + B 2 = 169

Since LHS = RHS, it is a right-angle triangle.
Given statement is false.
If the sides of a triangle are 13cm, 12cm and 5cm, then the given triangle is a right triangle.
Therefore, the correct answer is 2.

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