Statement-1: If the lengths of two sides of a triangle are roots of the equation `x^(2)-12x+35`=0 and the angle opposite to third side is obtuse, then the square of the length of the third side is greater than 74.
Statement- 2: In a `!ABC,cosC=(a^(2)+b^(2)-c^(2))/(2ab)`

Options

A. Statement-1 is True, Statement-2 is true, Statement-2 is a correct explanation for Statement-1.
B. Statement-1 is True, Statement-2 is True, Statement-2 is not a correct explanation for Statement-1.
C. Statement-1 is True, Statement-2 is False.
D. Statement-1 is False, Statement- 2 is True.

Explanation

Clearly, statement-2is true. (see cosine formulae in theory)
Clearly, x = 7, 5 are roots of the given equation. So, let a=7, b =5 be the lengths of two sides of `DeltaABC`. It is given that the angle C is obtuse.
`cosClt0`
`rArr(a^(2)+b^(2)-c^(2))/(2ab)lt0`
`rArrc^(2)gta^(2)+b^(2)rArrc^(2)gt49+25rArrc^(2)gt74`
So, statement-2 is also true and it is a correct explanation for statement-I.