Question

a rope is sq rt. 250 units long. If cut into 2 pieces so that the lengths of the pieces are in the ratio of 3:2 what is the length of longer piecein simplest radical form? 3:2 =5/3(?) Do i set x/sq.rt.250=5/3? I end up with 25 sq rt. 10/3. This isn't correct.

Answer 1

sqrt(250) = 5sqrt(10) (because you can simplify out 250 as (25 x 10), right?)

Now, let's just call "sqrt(10)" a variable, x, for a sec... so 5sqrt(10) is "5x"

If you cut a rope that is 5x long, and the two pieces have a ratio of 3:2, then one piece is 3x and the other is 2x.

So the longer piece is 3x... and since x is sqrt(10), the longer pieces should be 3sqrt(10)

Answer 2

ok that makes sense thanks

Answer 3

explain why you selected or knew to select sq rt. 10 as variable x

Answer 4

you don't have to do that... I just did it to help you see that you really had "5" of something.

If the problem had been, "cut a rope 5 feet long into 2 pieces with ratio 3:2, how long is the longer piece?" it would have seemed much easier.

The radical can sometimes confuse us :) but it is really just another number.

Answer 5

Without using the x, you could do it like this:

Answer 6

Hold on, I confused myself!! :)

Answer 7

3/5 * 5sqrt 10=3 sq rt 10????

Answer 8

yes, that is correct. are you unsure about it for some reason?

Answer 9

not now I understand. i was using 5/3 instead of 3/5

Answer 10

Good :)

I guess the way you could think of it is to recognize that if you need a ratio of 3:2, and you add the two parts together, then the smallest thing you could have is like 3 + 2 = 5, and the two parts have the right ratio, and the part lengths are 3/5 and 2/5. That would be for a rope of length 5. But the fractions are correct, so you just need to multiply times the actual rope length, which in this case was sqrt(250) = 5sqrt(10).

Glad you got it :)

Answer 11

thanks