Question

Triangles ABC and DEF have sides of lengths a, b, c and d, e, f respectively (symbols are as per usual notations). a, b, c and d, e, f satisfy the relation $\sqrt { a + b + c }$ $\sqrt { \mathrm { d } + \mathrm { e } + \mathrm { f } }$

= $\sqrt { \mathrm { ad } } + \sqrt { \mathrm { be } } + \sqrt { \mathrm { cf } }$, then

• A. Both the triangles ABC and DEF must be isosceles but not equilateral.
• B. Both the triangles ABC and DEF must be equilateral.
• C. Both the triangles ABC and DEF must be simillar but may not be congruent.
• D. Both the triangles ABC and DEF must be similar

Answer 1

Answer: (D)

Both the triangles ABC and DEF must be similar

Answer 2

$( \sqrt { \mathrm { ad } } + \sqrt { \mathrm { bc } } + \sqrt { \mathrm { cf } } ) ^ { 2 }$ ≤ (a + b + c)(d + e + f)

⇔ $\sqrt { \mathrm { ad } } + \sqrt { \mathrm { bc } } + \sqrt { \mathrm { cf } }$ ≤ $( \sqrt { a + b + c } )$ $( \sqrt { d + e + f } )$

The equality will take place if

\ triangle ABC and DEF must be similar.