Area of a rectangular rug

An oriental rug is 5 feet longer than it is wide.  The area is 12 ft².   To the nearest tenth of a foot, find its dimensions.

x = width
x + 5 = length

area of a rectangle is length x width

x(x + 5) = 12   {area is length x width}
x² + 5x = 12   {used distributive property}
x² + 5x - 12 = 0   {subtracted 12 from both sides}
a = 1, b = 5, c = -12   {the coefficients}

-b ± √(b² - 4ac)
--------------- = x {the quadratic formula}
          2a

-5 ± √(5² - 4(1)(-12))
------------------- = x   {substituted into the quadratic formula}
          2(1)

     -5 ± √(25 + 48)
--------------------- = x   {squared the 5 and multiplied}
               2

   -5 ± √73
------------- = x   {added 25 and 48}
          2

   -5 ± 8.5
------------ = x   {evaluated square root of 73}
        2

  -5 + 8.5
------------ = x   {dropped the -8.5, because width cannot be negative}
        2

  3.5
------ = x   {added -5 and 8.5}
    2

x = 1.75   {divided}
x + 5 = 6.75   {substituted 1.75, in for x, into x + 5}

width ≈ 1.8 ft
length ≈ 6.8 ft

Ask Algebra House