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1 year ago

a patio is shaped like a golden rectangle. it's length ( the longer side) is 16ft. what is the patios width? write your answer i

n simplified radical form.

Mathematics

1 answer:

Trava [24]1 year ago

3 0

$a\ golden\ rectangle:\ \ \ \frac{a+b}{a}= \frac{a}{b} \\----------------\\a+b=16\ [ft]\ \ \ \ \Rightarrow \ \ \ b=16-a\\\\ \frac{16}{a} = \frac{a}{16-a} \ \ \ \ \Leftrightarrow\ \ \ 16(16-a)=a^2\\\\a^2+16a-256=0\\\\\ \ \ \Rightarrow\ \ \ \Delta=16^2-4\cdot(-256)=256\cdot5\ \ \ \Rightarrow\ \ \ \sqrt{\Delta} =16 \sqrt{5} \\\\a_1= \frac{-16-16 \sqrt{5} }{2} =-8-8 \sqrt{5} 0\\\\$

$a=8( \sqrt{5} -1)\ \ \Rightarrow\ \ b=16-8( \sqrt{5} -1)=16-8\sqrt{5} +8=8(3- \sqrt{5} )\\\\Ans.\ This\ golden\ ractangle\ has\ sides:\\.\ \ \ \ \ \ \ 8( \sqrt{5} -1)\ [ft]\ \ and\ \ 8(3- \sqrt{5} )\ [ft]$

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Answer:

First option is correct.

Step-by-step explanation:

Let amounts of money James may have after he sees Rita be x.

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On combining equation (1) and (2), we get

$x=42.80\pm 12$

Subtract 42.80 from both sides.

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It can be written as

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igomit [66]

Answer:

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Step-by-step explanation:

We know that L*W= A

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Rus_ich [418]

Answer:

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Step-by-step explanation:

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In this problem, we have that:

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