From a point in the interior of an equilateral triangle, perpendiculars are drawn on the three sides. -Maths 9th

From a point in the interior of an equilateral triangle, perpendiculars are drawn on the three sides. -Maths 9th
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  Let each side of ㎝ equilateral triangle ABC be ′a′㎝ Now, ar△OAB=21​×AB×OP=21​×a×14=7a㎠→1 ar△OBC=​×BC×OQ =21​×a×10=5a㎠→2 ar△OAC=21​×AC×OR=21​×a×6=3a㎠→3 ∴ar△ABC=1+2+3=7a+5a+3a=15a㎠ Also area of equilateral triangle ABC=43​​a2 Now, 43​​a2=15a⇒a=3​15×4​×3​3​​=3603​​=203​㎝ Now, ar△ABC=43​​×(203​)2=3003​㎠
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