SOLUTION: A rug 4 meters by 5 meters covers 2/3 of the floor area in a room. The rug touches two walls, leaving a strip of uniform width around the other two walls. How wide is the strip?

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: A rug 4 meters by 5 meters covers 2/3 of the floor area in a room. The rug touches two walls, leaving a strip of uniform width around the other two walls. How wide is the strip?      Log On


   

Question 185108This question is from textbook
: A rug 4 meters by 5 meters covers 2/3 of the floor area in a room. The rug touches two walls, leaving a strip of uniform width around the other two walls. How wide is the strip? This question is from textbook

Answer by solver91311(24713) About Me  (Show Source):
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If the rug is 4 ft by 5 ft, then the area covered by the rug is 20 square feet, which is 2/3 of the unknown total area of the room, so:



So the area not covered by the rug is 30 - 20 = 10 square feet.

Let the width of the uncovered strip be x. The uncovered strip is an L shaped area that can be divided into three pieces. One piece is 5 ft by x feet, another piece is 4 feet by x feet, and the little piece in the corner is x feet by x feet. The area of the three pieces are 5x, 4x, and . The sum of the areas of these three pieces must be 10 square feet, thus:



Put in standard form:



Solve the quadratic by factoring and exclude the extraneous negative root. The positive root will be the width of the uncovered strip.

John