SOLUTION: mary and glen want to buy a rug tor a room that is 14 by 15 feet. They want to leave an even strip of flooring uncovered around the edges of the room. How wide a strip if they buy

Algebra ->  Surface-area -> SOLUTION: mary and glen want to buy a rug tor a room that is 14 by 15 feet. They want to leave an even strip of flooring uncovered around the edges of the room. How wide a strip if they buy       Log On


   

Question 916965: mary and glen want to buy a rug tor a room that is 14 by 15 feet. They want to leave an even strip of flooring uncovered around the edges of the room. How wide a strip if they buy a rug with an area of 110 square feet ?
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
Let w be the uniform width of uncovered floor.
Rug area is %2814-2w%29%2815-2w%29
Rug area is also given as 110 square feet.

%2814-2w%29%2815-2w%29=110, equality of the two area numbers
2%2A%287-w%29%2815-2w%29=55%2A2
%287-w%29%2815-2w%29=55
105-15w-14w%2B2w%5E2=55
50-29w%2B2w%5E2=0
highlight_green%282w%5E2-29w%2B50=0%29

You can try to factor that, or just use general formula for solution of quadratic equation.

w=%2829%2B-+sqrt%2829%5E2-4%2A2%2A50%29%29%2F%282%2A2%29
w=%2829%2B-+sqrt%28441%29%29%2F%282%2A2%29
w=%2829%2B-+21%29%2F4---- Only one of which should make sense.

cross%28w=12.5%29 or highlight%28w=2%29