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Question

a rope is raidcal 150 units long. the rope is cut into two piece, so that the lengths of the pieces are in the ratio 2:3. what is the length of the longer piece expressed in simplest radical form?

Answer 1

let

2 : 3 = ratio

2 + 3 = 5

2 / 5 = shorter length piece of rope

3/5 = longer length piece of rope

150 = total length of rope

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2/5(150)=

300 / 5 = 60

60 = shorter length

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3/5(150) =

450/5 = 90

90 = longer length

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The shorter length is 60 units

The longer length is 90 units

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Answer 2

2x + 3x = sqrt 150
5x = sqrt 150
x = (1/5)(sqrt 150)
x = (1/5)(sqrt (25*6))
x = (1/5)(5 sqrt 6)
x = sqrt 6

So the length of the pieces are
2 sqrt 6
and
3 sqrt 6