From the interior point O of an equilateral ABC, the sides bc , ac , and
From the interior point O of an equilateral ABC, the sides bc , ac , andPerpendiculars OD, OE and OF are drawn on ab, respectively, the lengths of these perpendiculars are 24 cm, 20, 22 cm respectively, find the area of
Step-by-step explanation:
Let each side of ㎝ equilateral triangle ABC be
′
a
′
㎝
Now, ar△OAB=
2
1
×AB×OP=
2
1
×a×14=7a㎠→1
ar△OBC=
×BC×OQ
=
2
1
×a×10=5a㎠→2
ar△OAC=
2
1
×AC×OR=
2
1
×a×6=3a㎠→3
∴ar△ABC=1+2+3=7a+5a+3a=15a㎠
Also area of equilateral triangle ABC=
4
3
a
2
Now,
4
3
a
2
=15a⇒a=
3
15×4
×
3
3
=
3
60
3
=20
3
㎝
Now, ar△ABC=
4
3
×(20
3
)
2
=300
3 ㎠