Question

a rectangular room is 3 meters longer than it is wide, and its perimeter is 22 meters. find the dimension of the room.
a. write an equation in terms of width, w, that models the situation.

b. solve the equation to find the dimensions of the rectangular room.
the length is
meters and the width is
meters.

Explanation:

Step1: Define length in terms of width

Let width = $w$. Length $l = w + 3$.

Step2: Set up perimeter equation

Perimeter of rectangle: $P = 2(l + w)$. Substitute $l = w+3$ and $P=22$:
$$2((w + 3) + w) = 22$$

Step3: Simplify and solve for $w$

Simplify inside parentheses: $2(2w + 3) = 22$
Divide both sides by 2: $2w + 3 = 11$
Subtract 3: $2w = 8$
Divide by 2: $w = 4$

Step4: Calculate length

Substitute $w=4$ into $l = w+3$:
$l = 4 + 3 = 7$

Answer:

A. $2(w + (w + 3)) = 22$ (or simplified: $4w + 6 = 22$)
B. The length is 7 meters and the width is 4 meters.