anonymous
  • anonymous
A cube has a surface area of 6x^2+60x+150. Find the length of the side.
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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chestercat
  • chestercat
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anonymous
  • anonymous
does x denote the length of the side?
anonymous
  • anonymous
ummmmm......I think so?
anonymous
  • anonymous
for a cube of side a, the surface area is 6a^2

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anonymous
  • anonymous
so 6x^2+60x+150 = 6a^2
anonymous
  • anonymous
if the problem just states what you have posted above, we cannot assume that the side of the cube is denoted by x, so thats why i am assuming it to be a. all you need to do now is get a in terms of x. so a^2 = x^2+10x+30, or a = sqrt(x^2+10x+30)
anonymous
  • anonymous
so what is the length of a side?
radar
  • radar
A cube surface area consist of 6 equal faces. Step 1. Divide your formula for total surface area by 6 and the new equation will be the surface area of one face. Dividing by 6 Gives you:\[x ^{2}+10x+25\]
anonymous
  • anonymous
whoops as radar says, it is 25, not 30.
radar
  • radar
Now factor that and get (x+5) (x=5) \[(x=5)^{2}\]
anonymous
  • anonymous
........
anonymous
  • anonymous
a = sqrt(x+5)^2 or a = x+5
radar
  • radar
\[(x+5)^{2}\]n Is what I meant to type
anonymous
  • anonymous
Thanks guys! But, how can I find out the length of a side from that?
radar
  • radar
dhatraditya called it the the length of the face is x+5 or the area is (x+5)^2
anonymous
  • anonymous
you can't. You can only find out length of the side in terms of x. So if you know x to be say,5 , then the side is 5+5 or 10.
anonymous
  • anonymous
Sigh......clear as mud. OMG!
anonymous
  • anonymous
OK lets start over. you are given that a cube has a surface area 6x^2+60x+150. if x is 1, then its surface area is 6(1)^2+60*1+150 so for x = 1, the surface area is 216. but we also know that the surface area of a cube in terms of the side of the cube is 6*side^2. so 6 * side^2 = 216 or side^2 = 36 or side = 6. Do you see the relationship between x and side? side is 6 and x is 1. so side is x+5. you can try it out with any x and you will always find side to be 5 more than x. Is that clearer?
anonymous
  • anonymous
Yes. Thanks. But......
anonymous
  • anonymous
in this problem, you just have to show the relationship between the side and x. suppose you had been given a problem which stated the surface area of a cube is 150. find the side of the cube, what would you have done to find the side? you would have plugged in 6*side^2 = 150 or side^2 = 25 or side =5. that is exactly what we are doing here. instead of 150, the surface area is 6x^2+60x+150. so 6*side^2 = 6x^2+60x+150. simplify it to get side in terms of x.
anonymous
  • anonymous
So........x+?=length of a side?
anonymous
  • anonymous
yes, we are finding out side in terms of x, it could be x+.. or x-.. or x*.. or x/.. depending on what the equation was. here it turned out that side was x+..
anonymous
  • anonymous
Lol, so what is it then?
anonymous
  • anonymous
as we wrote it earlier, side = x+5
anonymous
  • anonymous
Perfect!
anonymous
  • anonymous
okay let me give you an example. I say that x^2 is the area of a square of side x. what is x?
anonymous
  • anonymous
No clue.
anonymous
  • anonymous
thats because the equation a^2 is use to define a mathematical concept called square of side a. now, in your problem, someone had the brilliant idea to define the surface area of a cube in terms of x as 6x^2+60x+150. But we already have a standard method of defining the surface area of a cube as 6*side^2. so we find out what the x means in terms of the standard that we use to define the surface area of a cube i.e, the side of the cube.
anonymous
  • anonymous
hope that makes sense to you. squares, cubes, etc are just mathematical concepts, and we use certain equations to define these abstract concepts.
anonymous
  • anonymous
I appreciate your insight. Still a bit to wrap my mind around.
anonymous
  • anonymous
don't worry about it. You will understand what I mean as you progress. :)

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