SOLUTION: Cynthia Besch wants to buy a rug for a room that is 14 ft wide and 29 ft long. She wants to leave a uniform strip of floor around the rug. She can afford to buy 250 square feet of
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Question 1049572: Cynthia Besch wants to buy a rug for a room that is 14 ft wide and 29 ft long. She wants to leave a uniform strip of floor around the rug. She can afford to buy 250 square feet of carpeting. What dimensions should the rug have? Found 2 solutions by josgarithmetic, ikleyn:Answer by josgarithmetic(39616) (Show Source):
Area of the room, 14*29
Area of the border around the rug, 14*29-(14-2w)(29-2w)
Area of just the rug, (14-2w)(29-2w)
Area of just the rug is also given, 250 square feet.
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Cynthia Besch wants to buy a rug for a room that is 14 ft wide and 29 ft long.
She wants to leave a uniform strip of floor around the rug. She can afford to buy 250 square feet of carpeting.
What dimensions should the rug have?
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Let me show you another way of solving, without quadratic equations.
Notice that the difference "the length - the width" is 29-14 = 15 ft.
Since there is a uniform strip of floor around the rug, the difference of dimensions of the rug is the same, 15 ft.
Thus you need to determine the dimensions that have the difference of 15 and the product of 250 (square feet).
Can you guess them? - But of course, 25 x 10.
Answer. The rug should be 25 X 10 ft.
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