Math PROBLEM..PLEASE Help!!?

Question

i have this math problem, that i cant seem to figure out, can someone please help me.? the question goes as follows:

Question. A factory is to be built on a lot that measures 80m by 60m. A lawn of uniform width and equal in area to the factory must surround the factory. What demensions must the factory have?

Answer. It should have a uniform width of 10m
Factory is 60m x 40m


How would i figure that out?..any help would be great thanks

Answer 1

Let the dimensions of the factory be L and W. The area is LW.

The lawn surrounds the factory and has uniform width G. The area is

2LG + ( W - 2G ) G

That's the two long strips down the sides, length L, width G, plus the two leftover pieces at the top and bottom, length W - 2G and width G. A picture would be worth a thousand words here :)

So we now have

LW = 2LG + ( W - 2G ) G

We also know that half the lot is factory and half is lawn, so

LW = 1/2 ( 80 m ) ( 60 m )

Use the second equation to isolate either L or W and substitute into the first. Then you can solve for G as a fraction of W or L. Then use

L + 2G = 80

or

W + 2G = 60

to get the answers.

Answer 2

let x be the width of the lawn
then (80-2w)(60-2w)=2400
solve
4800 - 280w +4w^2 = 2400
4w^2 -280w +2400 = 0
w^2 - 70w +600 = 0
(w-60)(w-10)=0
w = 10 or 60
width cannot be 60 because it is only 60 width.
so width is 10
dimension of factory = 60 x 40