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\\n
Commented byMathsFan last updated on 20/Dec/21
$${help}\:{please} \\ $$
Answered by mr W last updated on 20/Dec/21
$${A}={xy}\:\Rightarrow{y}=\frac{{A}}{{x}} \\ $$ $${l}={x}+\mathrm{2}{y}={x}+\frac{\mathrm{2}{A}}{{x}}\geqslant\mathrm{2}\sqrt{{x}×\frac{\mathrm{2}{A}}{{x}}}=\mathrm{2}\sqrt{\mathrm{2}{A}} \\ $$ $${at}\:{least}\:{needed}\:\mathrm{2}×\sqrt{\mathrm{2}×\mathrm{128}}=\mathrm{32}{m} \\ $$
Commented byMathsFan last updated on 20/Dec/21
$${thank}\:{you}\:{Senior}\:{but}\:{can}\:{you}\:{make} \\ $$ $${it}\:{a}\:{bit}\:{comprehensive}\:{please}? \\ $$
Commented byTheSupreme last updated on 20/Dec/21
$$\frac{{x}_{\mathrm{1}} +{x}_{\mathrm{2}} }{\mathrm{2}}\geqslant\sqrt{{x}_{\mathrm{1}} {x}_{\mathrm{2}} } \\ $$
Commented bymr W last updated on 20/Dec/21
Commented byMathsFan last updated on 22/Dec/21
$${much}\:{appreciated}\:{sir} \\ $$