SOLUTION: A set of rectangle is constructed so that their sides are in the ratio length : width = 5 : √3 + 1 If the rectangle has a length of √2 metres, what is its width? (Pl

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Question 984753: A set of rectangle is constructed so that their sides are in the ratio length : width = 5 : √3 + 1
If the rectangle has a length of √2 metres, what is its width? (Please fully simplify and leave in surd form).
Answer by Boreal(15235) About Me  (Show Source):
You can put this solution on YOUR website!
Length/width=5/sqrt(3)+1
sqrt(2)/W=5/sqrt(3)+1
cross-multiply. sqrt(2)*sqrt(3)=sqrt(2*3)=sqrt(6)
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sqrt(6)+sqrt(2)=5W
W=(1/5)[sqrt (6)+ sqrt(2)]
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check: the ratio is approximately 5/2.7 or 1.85
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sqrt(6)+sqrt(2) is about 3.9, and that divided by 5, is 0.78, just less than 0.8.
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0.8*0.78=1.44, close enough to sqrt (2).