Question

The perimeter of a rectangular concrete slab is 114 feet and the area is 702 square feet. How do I write a quadratic equation to solve this?

Answer 1

Draw pictures, they will help you in pretty much every math problem you come across.


Now you can plug in one equation for the other to get an expression that tells you what one side is.

Answer 2

Ok, how would I start to solve for w though?

Answer 3

So if you want W then you can just use your area formula and divide both sides by L to get:

A/W=L

Then plug that into your perimeter formula:

P=2(A/W)+2W

Now you have enough information to solve for W. =)

Answer 4

I'm confused

Answer 5

What in particular is confusing, if you can narrow it down?

Answer 6

I don't really understand how to find l or w. I know the equations should be 2l+2w=114 and lw=702.

Answer 7

Ok, well you have two equations and two variables, so you can plug one equation into the other.

So when you see:

LW=702

you can divide both sides by W to get:

L=702/W

With me so far?

Now you have 2L+2W=114, and you have that other equation L=702/W so you can replace L with 702/W in the perimeter formula like this:

2L+2W=114
2(702/W)+2W=114

Does that make sense?

Now you can see that you have

1404/W+2W=114 and you can rearrange that to solve for W.

Answer 8

Ok, so far I understand that.

Answer 9

Cool, now you just need to solve the quadratic formula after rearranging what you just got into something that looks like:

ax^2+bx+c=0

Answer 10

So first, you would subtract 114 fro both sides? 1404/w+2w-114=114=114.

Answer 11

Yep except it all =0 now, not 114

Answer 12

1404/2+2w-114=0

Now you can multiply both sides by w and divide both sides by 2, try that out and show me what you get. It should make it look better. =D

Answer 13

1404/w+2w-114=0

whoops that's what I meant to write.