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

length ≈ 6.8 ft

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