Answer:
14 ft
Step-by-step explanation:
Given:
Let x = width of the bedroom:
Therefore:
[tex]\begin{aligned}\textsf{Area of a rectangle} & = \sf width \times length\\\implies 252 & = x(x+4)\\252 & = x^2+4x\\x^2+4x & = 252\end{aligned}[/tex]
To find the value(s) of x, complete the square.
Add the square of half the coefficient of the term in x to both sides:
[tex]\implies x^2+4x+\left(\dfrac{4}{2}\right)^2=252+\left(\dfrac{4}{2}\right)^2[/tex]
[tex]\implies x^2+4x+4=256[/tex]
Factor the perfect trinomial on the left side:
[tex]\implies (x+2)^2=256[/tex]
Square root both sides:
[tex]\implies x+2= \pm \sqrt{256}[/tex]
[tex]\implies x+2= \pm 16[/tex]
Therefore:
[tex]\implies x=-2+16=14[/tex]
[tex]\implies x=-2-16=-18[/tex]
As width cannot be negative, the width of the room is 14 ft.
