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A-gardener-wishes-to-make-a-rectangular-hen-run-of-area-128m-against-a-wall-which-is-to-serve-as-one-of-the-boundaries-Find-the-length-of-the-wire-netting-required-for-the-other-three-sides-




Question Number 161579 by MathsFan last updated on 19/Dec/21
  A gardener wishes to make a rectangular hen run of area 128m² against a wall which is to serve as one of the boundaries. Find the length of the wire netting required for the other three sides
$$ \\ $$A gardener wishes to make a rectangular hen run of area 128m² against a wall which is to serve as one of the boundaries. Find the length of the wire netting required for the other three sides
Commented by MathsFan last updated on 20/Dec/21
help please
$${help}\:{please} \\ $$
Answered by mr W last updated on 20/Dec/21
A=xy ⇒y=(A/x)  l=x+2y=x+((2A)/x)≥2(√(x×((2A)/x)))=2(√(2A))  at least needed 2×(√(2×128))=32m
$${A}={xy}\:\Rightarrow{y}=\frac{{A}}{{x}} \\ $$$${l}={x}+\mathrm{2}{y}={x}+\frac{\mathrm{2}{A}}{{x}}\geqslant\mathrm{2}\sqrt{{x}×\frac{\mathrm{2}{A}}{{x}}}=\mathrm{2}\sqrt{\mathrm{2}{A}} \\ $$$${at}\:{least}\:{needed}\:\mathrm{2}×\sqrt{\mathrm{2}×\mathrm{128}}=\mathrm{32}{m} \\ $$
Commented by MathsFan last updated on 20/Dec/21
thank you Senior but can you make  it a bit comprehensive please?
$${thank}\:{you}\:{Senior}\:{but}\:{can}\:{you}\:{make} \\ $$$${it}\:{a}\:{bit}\:{comprehensive}\:{please}? \\ $$
Commented by TheSupreme last updated on 20/Dec/21
((x_1 +x_2 )/2)≥(√(x_1 x_2 ))
$$\frac{{x}_{\mathrm{1}} +{x}_{\mathrm{2}} }{\mathrm{2}}\geqslant\sqrt{{x}_{\mathrm{1}} {x}_{\mathrm{2}} } \\ $$
Commented by mr W last updated on 20/Dec/21
Commented by MathsFan last updated on 22/Dec/21
much appreciated sir
$${much}\:{appreciated}\:{sir} \\ $$

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