If a, b, c are the sides of a triangle ABC, t | vedclass

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(D) To determine which inequality is not true,we can test with a specific triangle. Let the sides be $a = 2, b = 3, c = 4$. These satisfy the triangle

Vedclass · Accepted Answer

$abc \le (a + b - c)(b + c - a)(c + a - b)$

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(D) To determine which inequality is not true,we can test with a specific triangle. Let the sides be $a = 2, b = 3, c = 4$. These satisfy the triangle inequality $(2+3 > 4)$.For option $A$: $8(2)(3)(4) = 192$ and $(2+3)(3+4)(4+2) = 5 	imes 7 	imes 6 = 210$. Since $192 \le 210$,this is true.For option $B$: $3(2)(3)(4) = 72$ and $2^3 + 3^3 + 4^3 = 8 + 27 + 64 = 99$. Since $72 \le 99$,this is true.For option $C$: $6(2)(3)(4) = 144$ and $3(4)(3+4) + 4(2)(4+2) + 2(3)(2+3) = 12(7) + 8(6) + 6(5) = 84 + 48 + 30 = 162$. Since $144 \le 162$,this is true.For option $D$: $abc = 24$ and $(2+3-4)(3+4-2)(4+2-3) = (1)(5)(3) = 15$. Since $24 
ot\le 15$,this inequality is not true.

If $a, b, c$ are the sides of a triangle $ABC,$ then which of the following inequalities is not true?

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