Question

l3DABC and DDEF 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 $\sqrt { a + b + c }$

= $\sqrt { \mathrm { ad } }$ + $\sqrt { \mathrm { be } }$ + $\sqrt { \mathrm { cf } }$ , 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 similar but may not be congruent
• D. Both the triangle ABC and DEF must be similar

Answer 1

Answer: (D)

Both the triangle ABC and DEF must be similar

Answer 2

($\sqrt { \mathrm { ad } } + \sqrt { \mathrm { be } } + \sqrt { \mathrm { cf } }$)² £ (a + b + c) (d + e + f)

⇔ $\sqrt { \mathrm { ad } } + \sqrt { \mathrm { be } } + \sqrt { \mathrm { cf } }$ £ $( \sqrt { a + b + c } \sqrt { d + e + f }$

\ the equality will take place if $\frac { \mathrm { a } } { \mathrm { d } } = \frac { \mathrm { b } } { \mathrm { e } } = \frac { \mathrm { c } } { \mathrm { f } }$

\ triangle must be similar.