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?

Question

6188 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2017-07-17T02:39:51

See below

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

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

$A = 150 = x (2 x - 5)$ $A=150=x(2x-5)$

distribute $150 = 2 x^{2} - 5 x$ $" "150=2x^2-5x$

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

factor $(2 x + 15) (x - 10) = 0$ $" "(2x+15)(x-10)=0$

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

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