Question

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

Answer 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