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State if the following is true or false.

A triangle with sides (2a —1) cm, $2 2 a$ cm and (2a + 1) cm is a right angled triangle.

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True

False

answer is B.

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Detailed Solution

We are given a triangle with sides (2a -1) cm,

2 2 a

cm and (2a + 1) cm.
We know,
For a right-angled triangle, the Pythagoras theorem should be valid.
The Pythagoras Theorem is given as,

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

The square of the sides can be written as,

2 a − 1 2 = 4 a 2 − 4 a + 1 ⇒ 2 2 a 2 = 8 a ⇒ 2 a + 1 2 = 4 a 2 + 4 a + 1

Check whether the Pythagoras theorem is valid or not.
But the sum of the square of base and height is, (base = 2a-1 cm and height=2a+1 cm)

2 a − 1 2 + 2 a + 1 2 = 4 a 2 − 4 a + 1 + 4 a 2 + 4 a + 1 ⇒ 2 a − 1 2 + 2 a + 1 2 = 8 a 2 + 2

Hence the Pythagoras theorem is not valid and it is not a right-angled triangle.
It is not a right angled triangle.
Therefore, the statement is false.
The correct statement will be that a triangle with sides (2a -1) cm,

2 \sqrt{2} a

cm and (2a + 1) cm is not a right-angled triangle.
Hence, option 2 is correct.

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