Question

A cube has a surface area of 6x^2+60x+150. Find the length of the side.

Answer 1

does x denote the length of the side?

Answer 2

ummmmm......I think so?

Answer 3

for a cube of side a, the surface area is 6a^2

Answer 4

so 6x^2+60x+150 = 6a^2

Answer 5

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)

Answer 6

so what is the length of a side?

Answer 7

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:\[x ^{2}+10x+25\]

Answer 8

whoops as radar says, it is 25, not 30.

Answer 9

Now factor that and get (x+5) (x=5) \[(x=5)^{2}\]

Answer 10

........

Answer 11

a = sqrt(x+5)^2
or a = x+5

Answer 12

\[(x+5)^{2}\]n Is what I meant to type

Answer 13

Thanks guys! But, how can I find out the length of a side from that?

Answer 14

dhatraditya called it the the length of the face is x+5 or the area is (x+5)^2

Answer 15

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.

Answer 16

Sigh......clear as mud. OMG!

Answer 17

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?

Answer 18

Yes. Thanks. But......

Answer 19

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.

Answer 20

So........x+?=length of a side?

Answer 21

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+..

Answer 22

Lol, so what is it then?

Answer 23

as we wrote it earlier,
side = x+5

Answer 24

Perfect!

Answer 25

okay let me give you an example. I say that x^2 is the area of a square of side x. what is x?

Answer 26

No clue.

Answer 27

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.

Answer 28

hope that makes sense to you. squares, cubes, etc are just mathematical concepts, and we use certain equations to define these abstract concepts.

Answer 29

I appreciate your insight. Still a bit to wrap my mind around.

Answer 30

don't worry about it. You will understand what I mean as you progress. :)