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DeltaABC has different side lengths a,b,...

`DeltaABC` has different side lengths a,b,c. If `a^(2),b^(2),c^(2)` as sides form another `DeltaPQR`, then `DeltaABC` will always be

A

acute angled triangle only

B

obtuse angled triangle only

C

sometimes acute or sometimes obtuse depending on values of a,b nd c

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
A
Let `a gt b gt c`, given that `b+c gt a` and `b^(2)+c^(2)gt a^(2)`
`therefore b^(2)+c^(2)-a^(2)gt 0`
`therefore 2bc cos A gt 0`
`therefore cos A gt 0`
`therefore A` is acute angle.
Similarly `cos B gt 0, cos C gt 0`
So, `Delta ABC` is an acute angled triangle.
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