For reference: The image below represents a farm in the shape of an equilateral triangle, which is divided into $7$ fields by the $AL, BT,$ and $CR$ hedges, all having the same length. Fields like the $AMR$ measure $8$ hectares, and those that are like the $BNMR$, $22$ hectares. How big is the $MNP$ field? (Answer$5ha$)
My progress:
$AL = CR = BT \implies g+e+MN = g+e+PN+g+e+PM\\ \therefore \triangle PMN(equilateral\\ \frac{S_\triangle AMR}{S_\triangle PMN }= \frac{e.g}{x^2}\implies \frac{8}{S}=\frac{e.g}{x^2}\\ \frac{S_\triangle AMR}{S_\triangle LMC }= \frac{e.g}{(x+e).(x+g)}\implies \frac{8}{S+22}=\frac{e.g}{(x+e)(x+g)}\\ T.Menelaus: \triangle BCR-AL: b.(g+x).b = a.e.(a+b)\implies\\ b^2.(g+x)=a.e(l)\therefore l = \frac{b^2(g+x)}{ae}$
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