Question

A rectangular bedroom is 4 ft longer than it is wide. Its area is 252 ft2. What is the width of the room?

Answer 1

Answer:

14 ft

Step-by-step explanation:

Given:

• Bedroom is 4 ft longer than it is wide.
• Area is 252 ft².

Let x = width of the bedroom:

• width = x ft
• length = (x + 4) ft

Therefore:

$\begin{aligned}\textsf{Area of a rectangle} & = \sf width \times length\\\implies 252 & = x(x+4)\\252 & = x^2+4x\\x^2+4x & = 252\end{aligned}$

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:

$\implies x^2+4x+\left(\dfrac{4}{2}\right)^2=252+\left(\dfrac{4}{2}\right)^2$

$\implies x^2+4x+4=256$

Factor the perfect trinomial on the left side:

$\implies (x+2)^2=256$

Square root both sides:

$\implies x+2= \pm \sqrt{256}$

$\implies x+2= \pm 16$

Therefore:

$\implies x=-2+16=14$

$\implies x=-2-16=-18$

As width cannot be negative, the width of the room is 14 ft.