Question 122462: A rectangular rug 4m by 2m is placed in a room with floor area 24m^2 such that a strip of bare floor of uniform width surrounds the rug. Set up a function which models this situation and use it to algebraically determine the width of the strip of bare floor.
Answer by ankor@dixie-net.com(22740)   (Show Source):
You can put this solution on YOUR website! A rectangular rug 4m by 2m is placed in a room with floor area 24m^2 such that a strip of bare floor of uniform width surrounds the rug. Set up a function which models this situation and use it to algebraically determine the width of the strip of bare floor.
:
Draw this out, a rectangular rug inside a larger rectangle, label the width of
the bare floor around the outside of the rug as x. I will be apparent that the
dimensions of the larger rectangle will be (2x+4) by (2x+2)
:
The floor is area is given as 24 cu/m so we have an area equation of:
(2x+4)*(2x+2) = 24
FOIL
4x^2 + 8x + 4x + 8 = 24
:
4x^2 + 12x + 8 - 24 = 0
:
4x^2 + 12x - 16 = 0; our old friend, the quadratic equation!
:
Simplify, divide by 4:
x^2 + 3x - 4 = 0
:
Easily factors now to:
(x+4)(x-1) = 0
:
x = -4
and
x = +1, it's the positive solution we want here
:
A 1 meter uniform width around the rug
:
:
We can check this by finding the area with the calculated dimensions
2x = 2
(2+4) * (2+2) = 24
:
Did this make sense to you? Any questions?
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