Perimeter is 55 cm, find length of each side....

Question

anonymous · Answer

What shape?

anonymous · Answer

|dw:1328492778360:dw|

anonymous · Answer

rectange....trapezoid...?

anonymous · Answer

top: x+3  right: x^2-3x left: x+7 bottom: 3x-3

anonymous · Answer

quadralateral

anonymous · Answer

Okay! Perimeter is defined by all of the sides added together, right?

anonymous · Answer

I think so

anonymous · Answer

So: 
$$55=(x+3)+(x^2-3)+(x+7)+(3x-3)$$ 
55, the perimeter is equal to all of the sides added together! We can combine like terms...

anonymous · Answer

So then you have $$55=x^2+5x+4$$ I think.

anonymous · Answer

Can you solve for x?

anonymous · Answer

Oh no! I made a mistake. one moment.

anonymous · Answer

55=(x+3)+(x2−3x)+(x+7)+(3x−3)

anonymous · Answer

Which is then: x^2+2x+7

anonymous · Answer

Set it equal to 55 and solve.

anonymous · Answer

It says i need more than one answer, one for each side

anonymous · Answer

Each side of what?

anonymous · Answer

the quad

anonymous · Answer

Well if you solve for x, then you put x back into the equation for each side. Does that make sense?

anonymous · Answer

what is x? then i take that and put in each different equation?

anonymous · Answer

Yes. I can help you solve for x.

anonymous · Answer

ok thank you

anonymous · Answer

So, you have 55=(x+3)+(x^2−3x)+(x+7)+(3x−3). This simplifies when you combine like terms to 55=x^2+2x+7. Can you solve it from that point by factoring or do you need more help?

anonymous · Answer

I dont know, what do i do with 55? i can only solve the other side

anonymous · Answer

Well, we can set the expression equal to zero: 
Move the 55 over to the right. So now, we have 0=x^2+2x-48. Do you see how I got that? 

Next, try to factor this; it works out nicely. Should give you two answers.

anonymous · Answer

Yes, and ill solve that, be right back :)

anonymous · Answer

Good :)

anonymous · Answer

6 and -8?

anonymous · Answer

Yes! Okay, so we're talking about distance here. can we have a negative distance? Which solution do you think we should use?

anonymous · Answer

6

anonymous · Answer

Yes. So, what are your dimensions if you plug in x=6?

anonymous · Answer

i got 9, 13, 15, and 18 total, are these correct?

anonymous · Answer

That's what I got! Good work!

anonymous · Answer

:D thanks

anonymous · Answer

:D You're very welcome. Have a good night.