a rectangle fish pond is 8 feet longer than it is wide. a wooden walk 2ft wide is placed around the pond. the area covered by the pond and the walk is 160 ft squared greater than the area covered by the pond alone. what are the dimensions of the pond?

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Onlybetzyvid Onlybetzyvid

Mathematics

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a rectangle fish pond is 8 feet longer than it is wide. a wooden walk 2ft wide is placed around the pond. the area covered by the pond and the walk is 160 ft squared greater than the area covered by the pond alone. what are the dimensions of the pond?

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Crisforpid Crisforpid · Answer 1

Crisforpid Crisforpid

l = 8 + w ;
l * w + 160 = ( l + 2 ) * ( w + 2 ) => l * w + 160 = l * w + 2 * l + 2 * w + 4 => 156 = 2 * ( l + w ) => 78 = l + w; but, l = 8 + w => 78 = 8 + 2 * w => w = 70 / 2 => w = 35 feet; l = 8 + 35 => l = 43 feet.

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Kate200468id Kate200468id · Answer 2

Kate200468id Kate200468id

[tex]the\ fish\ pond:\\A_p=x\cdot (x+8)=x^2+8x\\\\the\ area\ covered\ by\ the\ walk:\\A_{w}=(x+2\cdot2)\cdot(x+8+2\cdot2)=(x+4)(x+12)=x^2+16x+48\\\\A_w=A_p+160\ \ \ \Rightarrow\ \ \ \ x^2+16x+48=x^2+8x+160\\\\16x-8x=160\ \ \ \Rightarrow\ \ \ 8x=160\ \ \ \Rightarrow\ \ \ x=20\\\\Ans.\ the\ width\ of\ the\ fish\ pond\ is\ 20\ ft\ and\ the\ length\ is\ 28\ ft[/tex]

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