Joan wants to buy a rug for a room that is 1111 feet by 1414 feet. she wants to leave a uniform strip of floor around the rug. she can afford 8888 square feet of carpeting. what dimensions should the rug have?

Solution:

Let x be the width of the strip.

Width of rug = 1111 - 2x

Length of rug = 1414 - 2x

Area of carpet = 8888

Area = Length * Width

8888 = (1414 - 2x) (1111 - 2x)

8888 = 1570954 - 2222x - 2828x + 4x²

4x² - 5050x + 1562066 = 0

2x² - 2525x + 781033 = 0

x = 720.5, 542

So, the value of x is 542.

Width of rug = 1111 - 2 (542) = 27

Length of rug = 1414 - 2 (542) = 330

Hence, the dimensions are 330, 27.