SOLUTION: In trapezoid ABCD, AC is a diagonal and ∠ABC≅∠ACD. Find AC if the lengths of the bases BC and AD are 12m and 27m respectively.

Algebra ->  Polygons -> SOLUTION: In trapezoid ABCD, AC is a diagonal and ∠ABC≅∠ACD. Find AC if the lengths of the bases BC and AD are 12m and 27m respectively.       Log On


   

Question 1134338: In trapezoid ABCD, AC is a diagonal and ∠ABC≅∠ACD. Find AC if the lengths of the bases BC and AD are 12m and 27m respectively.
Answer by MathLover1(20850) About Me  (Show Source):
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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%2FAC++=+AC%2FAD+
now, we can plug values
12%2FAC++=+AC%2F27+
AC%5E2=12%2A27
AC%5E2=324
AC=sqrt%28324%29
AC=18m