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-

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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

Commented by MathsFan last updated on 20/Dec/21

h e l p p l e a s e

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 = x y \Rightarrow y = \frac{A}{x}

l = x + 2 y = x + \frac{2 A}{x} ⩾ 2 \sqrt{x \times \frac{2 A}{x}} = 2 \sqrt{2 A}

a t l e a s t n e e d e d 2 \times \sqrt{2 \times 128} = 32 m

Commented by MathsFan last updated on 20/Dec/21

thank you Senior but can you make it a bit comprehensive please?

t h a n k y o u S e n i o r b u t c a n y o u m a k e

i t a b i t c o m p r e h e n s i v e p l e a s e ?

Commented by TheSupreme last updated on 20/Dec/21

\frac{x_{1} + x_{2}}{2} ⩾ \sqrt{x_{1} x_{2}}

Commented by mr W last updated on 20/Dec/21

Commented by MathsFan last updated on 22/Dec/21

m u c h a p p r e c i a t e d s i r

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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-

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