Answer:
[tex]AC=14\sqrt{2}m[/tex]
Step-by-step explanation:
we are given trapezoid ABCD
AC is a diagonal
∠ABC ≅ ∠ACD
we know that
BC and AD are parallel
so, <DAC = <ACB
so, ΔABC ≅ΔACD
Since, both triangles are similar
so, their ratios must be equal
we get
[tex]\frac{BC}{AC} =\frac{AC}{AD}[/tex]
now, we can plug values
[tex]\frac{14}{AC} =\frac{AC}{28}[/tex]
[tex]AC^2=14\times 28[/tex]
[tex]AC^2=14^2\times 2[/tex]
[tex]AC=14\sqrt{2}m[/tex]
