Question

B. In a blueprint, the length, 1, of a rectangular room is three times its width, w. The perimeter of the room must be greater than 120 feet. What are all the possible widths of the room?

Answer 1

The length of the room is l

since the length of the room is three times the width w so,

l=3w

The expression for the perimeter of rectangle is

$\text{Perimeter}=2(\text{length + Width)}$

Since perimetr is greater than the 120,

$\begin{gathered} 2(l+w)=P \\ 2(3w+w)>120 \\ 2(4w)>120 \\ 8w>120 \\ The\text{ perimetr inequality is }8w>120 \end{gathered}$

Inequality to represnt the statement the length, 1, of a rectangular room is three times its width, w is

$2(3w+w)>120$

solve for w,

$\begin{gathered} \text{ Since, 8w}>120 \\ w>15 \end{gathered}$

Thus, the value of w must be greater than 15.