the perimeter of the square is 208 in. Find the value of x

- anonymous

the perimeter of the square is 208 in. Find the value of x

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- anonymous

|dw:1439948377100:dw|

- anonymous

all 4 sides @Vocaloid and its 7x+3

- Vocaloid

hint:
4(side) = perimeter

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- anonymous

4+3=7?

- Vocaloid

side = ?

- anonymous

not getting you here?

- Vocaloid

what is the length of one side? look at the diagram...

- anonymous

(7x+3)in

- Vocaloid

right, and perimeter = ?

- anonymous

208in

- Vocaloid

good, so plug side and perimeter into the equation
4*(side) = perimeter

- anonymous

28+12 then =

- anonymous

40

- Vocaloid

not quite... you're forgetting the x

- Vocaloid

4(7x+3) = ?

- anonymous

40X

- Vocaloid

nope, still not quite right...

- Vocaloid

4(7x+3) = 4*(7x) + 4*(3) = ?

- anonymous

12

- Vocaloid

again, you're forgetting the x...
4*(7x) = __?

- anonymous

18x

- anonymous

28

- anonymous

x

- sammixboo

Well, since we know the perimeter is 208 inches, and one side is (7x +3) we can make an equation
208 = 4(7x+3)
208 is perimeter
4 is for all 4 sides
(7x+3) is the length of one side.
We gotta solve for x using this equation 208 = 4(7x+3), do you know how to do this?

- anonymous

yes

- anonymous

4*7=28 4*3=12 28+12=40 but that isnt it what am i doing wrong

- sammixboo

Great, so our first step would be is to simplify 4(7x + 3), which is what @Vocaloid was trying to explain. Do you know what distributing is?

- anonymous

yes

- sammixboo

You are close, just forgetting the x. Distributing is when you take the number on the outside of the parenthesis (in this case our number is 4) and multiply it by all the numbers INSIDE the parenthesis (which is 7x and 3)
So we have to multiply:
4 and 7x
4 and 3
We know that 4*3 is equal to 12, so we got that down. Now for 4*7x. We have to multiply the 4 and 7, but let's not forget about the x. After you multiplied 4 and 7, throw on the x on your answer. What is 4*7?

- anonymous

28

- anonymous

12

- sammixboo

Right, now we add the x, so our answer for 4*7x is 28x!
And we also know that:
4(7x + 3) = 28x + 12
Now let's continue on with our new equation, 208 = 28x + 12

- sammixboo

Do you know what our next step is for solving 208 = 28x + 12?

- anonymous

40 thats what i put up there

- anonymous

208=40

- sammixboo

Not quite. We have to use the order of operations and all that jazz

- anonymous

ohhhhhh

- anonymous

16

- sammixboo

We have to subtract 12 on both sides of the equation, since we are originally adding it. We have to isolate the x on one side of the equation, and this is our first step of solving this

- sammixboo

So, we have
208 - 12 = 28x + 12 - 12
208 - 12 = 28x
Can you tell me what is 208 - 12?

- anonymous

oh

- anonymous

7

- anonymous

thanks. :)

- sammixboo

Ah, right :) No problem. x = 7

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