Question

If the length of each side of a square is increased by 4 in., the area of the square becomes 9 times larger. Find the perimeter of the original square.

Answer 1

From the story you need to find an equation, that's the first step.

Answer 2

Yes, I agree, but how? I'm lost on how to set it up.

Answer 3

The story says something about the area of the square when you increase the sides. Let's a call the lenght of a side x. Then that area is (x+4)^2, right?

Answer 4

Yes, that's right. So do I then foil that? Would that be my first step?

Answer 5

You're going to have to do that sooner or later, but first I would find the equation from the story, so (x+4)^2 = ?

Answer 6

I don't know. It didn't give me what it equals. It only said the area of the square will then be 9 times larger.

Answer 7

You can get the equation from that bit of information.

Answer 8

Would it be 9x, then?

Answer 9

Almost, we're talking about area...

Answer 10

Remember x was the lenght of a side, so 9x would be 9 times the length of a side, but we want 9 times the area.

Answer 11

I don't 9x squared is right, is it?

Answer 12

Sorry... been working on algebra word problems for a few hours and am a little out of it, as far as thinking 100% goes.

Answer 13

No problem, so 9 x^2 indeed

So we get (x+4)^2=9x^2

Answer 14

Then I will set it all equal to zero, right?

Answer 15

Hold on, you mean (x+4)^2-9x^2=0 I suppose?

Answer 16

Yes, sir, that's what I mean.

Answer 17

Great, that's a good Idea.

Answer 18

Can you solve for x?

Answer 19

So far, I have -8(x-2)(x+1)=0.

Answer 20

looks good.

Answer 21

When setting it equal to 0, what happens to the -8? How does that affect the answer? Does that even make sense?

Answer 22

I have x=2, -1, but I didn't use the -8 part.... so am I not done with the problem?

Answer 23

It makes sense and it doesn't affect the answer: you can divide both sides by -8 to get (x-2)(x+1)=0

Answer 24

So therefore, my answer is x=2 and x=-1?

Answer 25

We're not done yet. The question was to compute the perimeter, not length of a side. Also are you sure both x=2 and x=-1 make sense? (You've solved the equation correctly)

Answer 26

I won't use the x=-1. I'll cross it out, so to speak, and just work with the x=2, correct?

Answer 27

right

Answer 28

So now I'll just plug my 2 in for any x in the original equation?

Answer 29

You could do that, and see that it is in fact a solution to the equation, but I wouldn't do that here.

You've found the length of one side, you want to find the perimeter of the square, so...

Answer 30

The perimeter would be 8. Because 2x4=8, correct?

Answer 31

That's right.

Answer 32

Thank you! :D

Answer 33

Yay, you're welcome!

Answer 34

Am I supposed to press "good answer" on the answers where you helped me? Does that give you more points or something? (I'm totally new to this, which I'm sure you could tell.)

Answer 35

You could that, I'd get a medal. But I'm not exactly aching to get them :)

Answer 36

After you get some medals you level up.

Answer 37

:) Okay. Thank you again! I really appreciateed the help!