You can
put this solution on YOUR website! I need help with the dimensions of
a strip of flooring around a rug.
Catarina and Jose want to buy a rug
for a room that is 15 feet by 20 feet.
They want to leave an even strip of
flooring uncovered around the edges
of the room. how wide a strip will
they have if they buy a rug with an
area of 234 square feet?
_x________________________x_
| | | |x
|___|____________________|___|
| | 20-2x | |
| | 15-2x| |
| | | |
|___|____________________|___|
|x | | |x
|___|____________________|___|
Area of rug = 234
Area of rug = LW = (20-2x)(15-2x)
so,
(20-2x)(15-2x) = 234
Use FOIL:
300 - 40x - 30x + 4x² = 234
300 - 70x + 4x² = 234
4x² - 70x + 300 = 234
4x² - 70x + 66 = 0
Divide thru by 2
2x² - 35x + 33 = 0
(x - 1)(2x - 33) = 0
x = 1, x = 16.5
The larger value is impossible, so the
only feasible answer is a 1 foot strip.
Edwin
