SOLUTION: I've been working on this problem for 5 days and can't figure it out. This is the question. "A homeowner has poured a rectangular slab for a barbecue pit. The length is 3 feet more

Question 367018: I've been working on this problem for 5 days and can't figure it out. This is the question. "A homeowner has poured a rectangular slab for a barbecue pit. The length is 3 feet more than its width. It is surrounded by a 2 foot wide flower bed. If the area covered by both is 270 square feet, find the dimensions of the barbecue area".
1. A=lw which would mean that the with is 15 and the length is 18 (18*15=270). Now if you subtract the perimeter of that, which would be 8 feet (2*4=8) that would mean that the remaining area would be 262.
2. At 51 I suck at word problems as bad as I did when I was 15 and just can not figure out how to put this in a quadratic equation. I have tried 270=(w+3)(w)-2^2 and it doesn't work.
I have tried x=(w+3)(w)-2^2-270 and that doesn't work.
What exactly is it that I'm doing wrong?
3. Yes, this is a homework problem and yes I have tried everything to solve it. I have read and re-read the chapter and my class notes but it just comes down to I don't understand...Please Help!!!1
Susan Lucas
Found 2 solutions by Fombitz, solver91311:
Answer by Fombitz(32388) (Show Source): You can put this solution on YOUR website!

The outer edges of the pit and flower bed are then,
and
or
and
.
.

Two solutions but only the positive one makes sense.

ft
Then

ft
The barbeque pit is 13 ft by 16 ft.
Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!

What you are doing wrong is guessing. You lucked out and guessed the outer dimensions from which you could have simply subtracted 4 feet (2 foot wide flower bed all around) to get the slab dimensions. But in general this would have been a poor strategy for this sort of problem if you had been given dimensions that did not come out to nice round numbers.

Let's try a systematic approach:

Let represent the width of the slab. Then must represent the length of the slab. Since the flower bed is two feet wide and hence adds two feet to EACH side and EACH end of the overall area. That means that the width dimension of the outside edge of the flower bed is and the length dimension must be .

Using , and knowing that the overall area is 270, we can write:

A little algebra gets us to:

Solve the quadratic for . Discard the negative root since we are looking for a positive measure of length. The positive root is the width of the concrete slab and 3 more is the length.

John

My calculator said it, I believe it, that settles it

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