Areas of triangles are in the ratio 81:16 but the sides of two similar triangle is

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1. Step-by-step explanation:

   16:11

   Let us have two similar triangles ΔABC and ΔDEF as shown below. As they are similar, we have

   ABDE=ACDF=BCEF

   Let us also draw perpendiculars AP and DQ from A and D respectively on to BC and EF as shown.

   

   It is apparent that ΔAPB and ΔDEQ are also similar as all respective angles are equal. Hence,

   ABDE=APDQ=BPEQ

   We also have ΔABC=12×BC×AP and ΔDEF=12×EF×DQ and

   ΔAPBΔDEQ=BC×APEF×DQ=BCEF×APDQ

   But APDQ=ABDE

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