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# The length of a rectangular floor is 5 feet less than twice its width. The area of the rectangle is 150 square feet. What is the length of the room?

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Jul 17, 2017

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width $= 10$ feet
length $= 15$ feet

#### Explanation:

Area = length X width
let width $w = x$
let length $l = 2 x - 5$

$A = 150 = x \left(2 x - 5\right)$

distribute $\text{ } 150 = 2 {x}^{2} - 5 x$

subtract 150 from both sides $\text{ } 150 - 150 = 2 {x}^{2} - 5 x - 150$

factor $\text{ } \left(2 x + 15\right) \left(x - 10\right) = 0$

width $x = 10 \text{ }$ or $x = - \frac{15}{2}$
since distance cannot be negative, $\text{ } x = 10$

width $= 10$ feet
length $= 2 \cdot 10 - 5 = 15$ feet

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