SOLUTION: Cynthia Besch wants to buy a rug for a room that is 22 ft wide and 27 ft long. She wants to leave a uniform strip of floor around the rug. She can afford to buy 204 square feet of

Question 1085610: Cynthia Besch wants to buy a rug for a room that is 22 ft wide and 27 ft long. She wants to leave a uniform strip of floor around the rug. She can afford to buy 204 square feet of carpeting. What dimensions should the rug have?
Answer by ikleyn(52847) (Show Source): You can put this solution on YOUR website!
.

(22-2x)*(27-2x) = 204.

Solve this quadratic equation by any method you want/you know.


I am solving it MENTALLY in this way.

204 = 4*51 = 12*17.       (*)


The factors (22-2x) and (27-2x) differ in 5 units: (27-2x) - (22-2x) = 5.

From the other side, (*) gives the decomposition of 204 into the product of 2 factors that differ in 5 units: 204 = 12*17 and 17-12 = 5.


Based on it, I conclude that 22-2x = 12. Hence, 2x = 22 - 12 = 10. Which means that x = 5, the uniform wide of the strip.


Answer. The rug dimensions are 22 - 2*5 = 12 feet  and  27 - 2*5 = 17 feet.

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