Question 1134338


we are given trapezoid {{{ABCD}}}

{{{AC}}} is a diagonal

∠ {{{ABC}}} ≅ ∠ {{{ACD}}}

we know that 

{{{BC}}} and {{{AD}}} are parallel

so, < {{{DAC}}} = < {{{ACB}}}

so, Δ {{{ABC}}} ≅ Δ {{{ACD}}}

Since, both triangles are similar 

so, their ratios must be equal 

we get 

{{{BC/AC  = AC/AD }}}

now, we can plug values

{{{12/AC  = AC/27 }}}

{{{AC^2=12*27}}}

{{{AC^2=324}}}

{{{AC=sqrt(324)}}}

{{{AC=18m}}}