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

-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


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